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1: GST [Goods and Service Tax]
2: Banking (Recurring Deposit Account)
3: Shares and Dividend
Unit 2. Algebra
4: Linear Inequations (In one variable)
5: Quadratic Equations
6: Solving (simple) Problems (Based on Quadratic Equations)
7: Ratio and Proportion (Including Properties and Uses)
8: Factorization of Polynomials (Remainder and Factor Theorems)
9: Matrices
10: Arithmetic Progression
11: Geometric Progression
Unit 3. Co-ordinate Geometry
12: Reflection
13: Section Formula and Mid-Point Formula
14: Equation of a Line
Unit 4. Geometry
15: Similarity (With Applications to Maps and Models)
16: Loci (Locus and Its Constructions)
17: Circles
18: Tangents and Intersecting Chords
19: Constructions (Circles)
Unit 5. Mensuration
▶ 20: Cylinder, Cone and Sphere
Unit 6. Trigonometry
21: Trigonometrical Identities
22: Height and Distances
Unit 7. Statistics
23: Graphical Representation
24: Measure of Central Tendency (Mean, Median, Quartiles and Mode)
25: Probability
![Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 20 - Cylinder, Cone and Sphere - Shaalaa.com](/images/concise-mathematics-english-class-10-icse_6:7eb8c97e7ccc4a1c956f7ac8305d25e3.jpg "Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 20 - Cylinder, Cone and Sphere")
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Solutions for Chapter 20: Cylinder, Cone and Sphere
Below listed, you can find solutions for Chapter 20 of CISCE Selina for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई.
Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई 20 Cylinder, Cone and Sphere EXERCISE 20 (A) [Pages 304 - 306]
Multiple Choice Type: Choose the correct answer from the options given below.
An open hollow cylindrical container, made of very thin metal sheet, has radius r cm and height h cm, its total surface area (in cm2) is ______.
πr2h + 2πrh
4πrh + πr2
4πrh + 2πr2
2πrh + 2πr2
The curved area of a solid cylinder is S cm2 and the circumference of its base is C cm; the height of the cylinder is ______.
C × S
C + S
S ÷ C
S − C
A cylindrical container has sufficient water to submerge a solid cubical object of its each edge a cm. If the radius of the container is r cm, the rise in level (h cm) of water in the container is ______.
\[\sqrt{\frac{a^{3}}{\pi r}}\]
\[\frac{a}{\sqrt{\pi r}}\]
\[\frac{a^{3}}{\pi r^{2}}\]
\[\frac{\pi r^{2}}{a}\]
A solid cylinder of radius R cm and height H cm is melted and recast into smaller identical solid cylinders of height h cm and radius r cm. The number of smaller solid cylinders obtained is ______.
\[\frac{\mathrm{RH}}{r h}\]
\[\frac{\mathrm{R}^{2} \mathrm{H}}{r^{2} h}\]
\[\mathrm{R}^{2} \mathrm{H} \div r^{2} h^{2}\]
\[\frac{\mathrm{RH}^{2}}{r h}\]
The total surface area of an open pipe of length H cm, external radius R cm and internal radius r cm, is ______.
πR2 − πr2 + 2π(R − r) H
2πR2 − 2πr2 + 2πRH
2πRH − 2πrh + πR2 − πr2
2(πR2 − πr2) + 2πRH + 2πrH
The inner radius of a pipe is 2.1 cm. How much water can 12 m of this pipe hold?
How many cubic meters of earth must be dug out to make a well 28 m deep and 2.8 m in diameter? Also, find the cost of plastering its inner surface at Rs. 4.50 per sq.meter.
What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?
A cylinder has a diameter of 20 cm. The area of the curved surface is 100 cm2 (sq. cm). Find:
- the height of the cylinder correct to one decimal place.
- the volume of the cylinder correct to one decimal place.
A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find the weight, in kilogram, of 2 metres of the pipe if 1 cm3 of the metal weights 7.7 g.
A cylindrical container with diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 22 cm × 14 cm × 10.5 cm. Find the rise in the level of the water when the solid is submerged.
A cylindrical container with internal radius of its base 10 cm, contains water up to a height of 7 cm. Find the area of the wet surface of the cylinder.
Find the total surface area of an open pipe of length 50 cm, external diameter 20 cm and internal diameter 6 cm.
The height and the radius of the base of a cylinder are in the ratio 3 : 1. If it volume is 1029 π cm3; find it total surface area.
The radius of a solid right circular cylinder decreases by 20% and its height increases by 10%. Find the percentage change in its : volume
The radius of a solid right circular cylinder decreases by 20% and its height increases by 10%. Find the percentage change in its : curved surface area.
Find the minimum length in cm and correct to nearest whole number of the thin metal sheet required to make a hollow and closed cylindrical box of diameter 20 cm and height 35 cm. Given that the width of the metal sheet is 1 m. Also, find the cost of the sheet at the rate of Rs. 56 per m.
Find the area of metal sheet required, if 10% of it is wasted in cutting, overlapping, etc.
3080 cm3 of water is required to fill a cylindrical vessel completely and 2310 cm3 of water is required to fill it upto 5 cm below the top. Find :
- radius of the vessel.
- height of the vessel.
- wetted surface area of the vessel when it is half-filled with water.
Find the volume of the largest cylinder formed when a rectangular piece of paper 44 cm by 33 cm is rolled along its :
- shorter side.
- longer side.
A metal cube of side 11 cm is completely submerged in water contained in a cylindrical vessel with diameter 28 cm. Find the rise in the level of water.
A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embankment 2 m in width and 1.6 m in height. Find the depth of the circular tank.
The sum of the heights and the radius of a solid cylinder is 35 cm and its total surface area is 3080 cm2, find the volume of the cylinder.
The total surface area of a solid cylinder is 616 cm2. If the ratio between its curved surface area and total surface area is 1 : 2; find the volume of the cylinder.
A cylindrical vessel of height 24 cm and diameter 40 cm is full of water. Find the exact number of small cylindrical bottles, each of height 10 cm and diameter 8 cm, which can be filled with this water.
Two solid cylinders, one with diameter 60 cm and height 30 cm and the other with radius 30 cm and height 60 cm, are metled and recasted into a third solid cylinder of height 10 cm. Find the diameter of the cylinder formed.
The total surface area of a hollow cylinder, which is open from both the sides, is 3575 cm2; area of its base ring is 357.5 cm2 and its height is 14 cm. Find the thickness of the cylinder.
Two right circular solid cylinders have radii in the ratio 3 : 5 and heights in the ratio 2 : 3. Find the ratio between their curved surface areas.
Two right circular solid cylinders have radii in the ratio 3 : 5 and heights in the ratio 2 : 3. Find the ratio between their volumes.
A closed cylindrical tank, made of thin ironsheet, has diameter = 8.4 m and height 5.4 m. How much metal sheet, to the nearest m2, is used in making this tank, if `1/15` of the sheet actually used was wasted in making the tank?
Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई 20 Cylinder, Cone and Sphere EXERCISE 20 (B) [Page 310]
Multiple Choice Type: Choose the correct answer from the options given below.
The radius and height of a solid metallic cone are r cm each. The volume of the cone is:
\[\frac{1}{3} \pi r^{2}\]
\[\frac{4}{3} \pi r^{2}\]
\[\frac{1}{3} \pi r^{3}\]
\[\frac{4}{3} \pi r^{3}\]
The radius of the base of a solid cone is r cm and its height is h cm; its curved surface area is ______.
\[\pi \times r \times \sqrt{h^{2}-r^{2}}\]
\[\pi \times r \times \sqrt{h^{2}+r^{2}}\]
\[\pi \times r \times(h+r)\]
\[\pi r^{2}(h+r)\]
A conical toy tent-house, 28 cm in radius and 21 cm in slant height, is made from a rectangular sheet of paper 22 cm wide. The smallest length of the paper sheet required is:
84 cm
42 cm
72 cm
140 cm
For a cone, the ratio between the volume and area of its base is 11: 6. The height of the cone is:
\[1 \frac{5}{6}\] units
5.5 units
11 units
5 units
The radii of two solid cones are equal and their slant heights are in the ratio 7 : 4. The ratio between their curved surface areas is:
4 : 7
7 : 4
16 : 49
49: 16
Find the volume of a cone whose slant height is 17 cm and radius of base is 8 cm.
The curved surface area of a cone is 12320 cm2. If the radius of its base is 56 cm, find its height.
The circumference of the base of a 12 m high conical tent is 66 m. Find the volume of the air contained in it.
The radius and the height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the radius and slant height of the cone. (Take π = 3.14)
The diameter of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surface areas.
There are two cones. The curved surface area of one is twice that of the other. The slant height of the latter is twice that of the former. Find the ratio of their radii.
A heap of wheat is in the form of a cone of diameter 16.8 m and height 3.5 m. Find its volume. How much cloth is required to just cover the heap?
If you are given a rectangular canvas of 1.5 m in width, what length of this canvas would you require to make a conical tent that is 48 m in diameter and 7 m in height? Note that 10% of the canvas is used (wasted) in folds and stitchings.
Also, find the cost of the canvas at the rate of 24 per metre.
A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed.
The total surface area of a right circular cone of slant height 13 cm is 90π cm2.
Calculate:
- its radius in cm.
- its volume in cm3. [Take π = 3.14].
The area of the base of a conical solid is 38.5 cm2 and its volume is 154 cm3. Find the curved surface area of the solid.
A vessel, in the form of an inverted cone, is filled with water to the brim. Its height is 32 cm and diameter of the base is 25.2 cm. Six equal solid cones are dropped in it, so that they are fully submerged. As a result, one-fourth of water in the original cone overflows. What is the volume of each of the solid cones submerged?
The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the:
- radius of the floor
- height of the tent
- length of the canvas required to cover this conical tent if its width is 2 m.
Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई 20 Cylinder, Cone and Sphere EXERCISE 20 (C) [Page 313]
Multiple Choice Type: Choose the correct answer from the options given below.
A solid metallic sphere of radius 16 cm is melted to form small identical spheres each of diameter 4 cm. The number of spheres formed is:
64
252
512
1024
A hemi-spherical bowl (as shown) has external radius R and internal radius r, the outer surface area of the bowl is ______.
2πR2 + πr2
3πR2 − πr2
2πR2 + 2πr2
2πR2 − πr2
The ratio between the volumes of two spherical solids is 27 : 8. The ratio between their curved surface areas is :
27 : 8
8 : 27
3 : 2
9 : 4
A solid metallic sphere of radius 8 cm is melted and recast into 64 identical solid spheres. The diameter of each smaller sphere formed is:
4 cm
2 cm
8 cm
1 cm
r1, r2 and r3 are the radii of three metallic spheres. If these spheres are melted to form a single solid sphere, the radius of sphere formed is:
\[\sqrt{r_{1}^{3}+r_{2}^{3}+r_{3}^{3}}\]
\[r_{1}+r_{2}+r_{3}\]
\[r_{1}^{3}+r_{2}^{3}+r_{3}^{3}\]
\[\sqrt[3]{r_{1}^{3}+r_{2}^{3}+r_{3}^{3}}\]
The volume of a sphere is 38808 cm3; find its diameter and the surface area.
A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?
How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?
The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :
- radii,
- surface areas.
If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere?
A solid metal sphere is cut through its center into 2 equal parts. If the diameter of the sphere is `3 1/2 cm`, find the total surface area of each part correct to two decimal places.
The internal and external diameter of a hollow hemispherical vessel are 21 cm and 28 cm respectively. Find :
- internal curved surface area,
- external curved surface area,
- total surface area,
- volume of material of the vessel.
A solid sphere and a solid hemi-sphere have the same total surface area. Find the ratio between their volumes.
Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted and recasted into a single solid sphere. Taking π = 3.1, find the surface area of the solid sphere formed.
Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई 20 Cylinder, Cone and Sphere EXERCISE 20 (D) [Page 315]
Multiple Choice Type: Choose the correct answer from the options given below.
A cone and a sphere have equal volumes. Their radii are also equal each being 10 cm; the height of the cone is:
70 cm
40 cm
50 cm
20 cm
A sphere and a cone have equal volumes and equal radii. The ratio between the radius and height of the cone is:
3 : 4
4 : 3
4 : 1
1 : 4
The radius and the height of a cone are in the ratio 2 : 1. The ratio between the volumes of a sphere and this cone (both having equal radii) is:
1 : 4
4 : 1
8 : 1
1 : 8
A solid metallic cylinder is melted and formed into identical solid cones each having same radius and same height as that of the cylinder. The number of cones formed is:
3
6
9
2
A solid metallic cone of radius 10 cm and height 12 cm is melted to form a wire of uniform area of cross-section 1 cm2. The length of wire formed is:
40 × π cm
4 × π m
400 × π m
2 × π m
A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cone of height 32 cm. Find the diameter of the base of the cone.
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.
A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl?
The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate :
- the radius of the solid sphere.
- the number of cones recast. [Take π = 3.14]
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate:
- the radius of the sphere.
- the number of cones recast. (Take π = `22/7`)
Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई 20 Cylinder, Cone and Sphere EXERCISE 20 (E) [Pages 319 - 320]
Multiple Choice Type: Choose the correct answer from the options given below.
In the given figure, the radius of the cone is same as its height equal to 2 cm each. The volume of the whole body is:
8π cm3
16 cm³
32π сm3
32 cm3
In the given figure, height of the conical part is 3 cm. The radius and the height of the cylindrical part are 1 cm each. The total volume of the body is:
9π cm3
18π cm3
2π сm3
4π cm3
The given figure shows a solid cylinder of height h cm and radius r cm. If the slant height of the conical cavity is l cm, the total surface area of the remaining solid is:
πrl + 2πrh + 2πr2
πr2+ πrl + 2πrh
2πr2 − πrl + 2πrh
(πrl + πr2) + 2r2 + 2πrh
In the given figure, a solid cone is kept inverted in a closed cylindrical container such that the height of cone = height of cylinder = h, radius of cone = radius of cylinder = r and slant height of cone = l. If the remaining of cylinder is completely filled with water, the wetted surface area of the whole body is:
2πrh + πr2 + πrl
2πrh + πrl
2πrh + 2πr2 + πrl
2πrh − πr2 + πrl
The given figure shows a solid sphere and a closed cylindrical container, both having the same height and same radii. The volume of air left in the cylinder is:
6πr3
3/2πr3
2/3πr3
4πr3
A cone of height 15 cm and diameter 7 cm is mounted on a hemisphere of same diameter. Determine the volume of the solid thus formed.
A buoy is made in the form of hemisphere surmounted by a right cone whose circular base coincides with the plane surface of hemisphere. The radius of the base of the cone is 3.5 metres and its volume is two-third of the hemisphere. Calculate the height of the cone and the surface area of the buoy, correct to two places of decimal.
From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find :
- the surface area of remaining solid,
- the volume of remaining solid,
- the weight of the material drilled out if it weighs 7 gm per cm3.
A cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.
The radii of the bases of two solid right circular cones of same height are r1 and r2 respectively. The cones are melted and recast into a solid sphere of radius R. Find the height of each cone in terms r1, r2 and R.
A cone and a hemisphere have the same base and the same height. Find the ratio between their volumes.
Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई 20 Cylinder, Cone and Sphere EXERCISE 20 (F) [Page 323]
Multiple Choice Type: Choose the correct answer from the options given below.
The volume of a solid cylinder and a solid cone are same. If their radii are also same, the ratio between the heights of cylinder and cone is:
3 : 1
2 : 3
1 : 3
3 : 2
The volume of the given solid is:
\[\frac{4}{3} \pi r^{3}\]
\[\frac{4}{3} \pi r^{2}\]
\[2 \pi r^{3}\]
\[4 \pi r^{3}\]
Eight identical metallic spheres, each of radius 1 cm are melted and recast into a solid sphere. The radius of the solid sphere formed is:
3 cm
2 cm
1.5 cm
2.5 cm
The ratio between the heights of two solid cones is 2 : 3 and ratio between their radii is 9 : 8. The ratio between their volumes is:
27 : 32
32 : 27
3 : 2
2 : 3
The radius of a solid cylinder is doubled keeping the height same. The percentage increase in its volume is:
200%
100%
400%
300%
From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base is removed. Find the volume of the remaining solid.
From a solid cylinder whose height is 16 cm and radius is 12 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume and total surface area of the remaining solid.
A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 80 m, calculate the total area of canvas required. Also, find the total cost of canvas used at Rs. 15 per metre if the width is 1.5 m.
A circus tent is cylindrical to a height of 8 m surmounted by a conical part. If total height of the tent is 13 m and the diameter of its base is 24 m; calculate :
- total surface area of the tent,
- area of canvas, required to make this tent allowing 10% of the canvas used for folds and stitching.
A cylindrical container with diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 22 cm × 14 cm × 10.5 cm. Find the rise in the level of the water when the solid is submerged.
Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
An open cylindrical vessel of internal diameter 7 cm and height 8 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is `3 1/2` cm and height 8 cm. Find the volume of water required to fill the vessel. If this cone is replaced by another cone, whose height is `1 3/4` cm and the radius of whose base is 2 cm, find the drop in the water level.
A cylindrical can, whose base is horizontal and of radius 3.5 cm, contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can, calculate:
- the total surface area of the can in contact with water when the sphere is in it;
- the depth of water in the can before the sphere was put into the can.
A hollow cylinder has solid hemisphere inward at one end and on the other end it is closed with a flat circular plate. The height of water is 10 cm when flat circular surface is downward. Find the level of water, when it is inverted upside down, common diameter is 7 cm and height of the
cylinder is 20 cm.
Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई 20 Cylinder, Cone and Sphere TEST YOURSELF [Pages 324 - 326]
Multiple Choice Type: Choose the correct answer from the options given below.
The given figure shows a solid cylinder and a solid cone on it according to the given measurement, the total surface area of the solid in terms of π and r is:
4πr2
5πr2
6πr2
7πr2
The radii of two solid spheres are 10 cm and 20 cm. The ratio between their volumes is:
3 : 8
1 : 4
1 : 8
8 : 3
A cone and a sphere have equal volumes. If height of the cone = radius of the sphere =10 cm, the radius of the cone is:
40 cm
10 cm
30 cm
20 cm
A solid metal cuboid with dimensions 10 cm, 11 cm and 8 cm is melted and identical solid spheres, each of radius 1 cm, are formed. The number of spheres formed is:
105
210
315
420
By applying force on an uniform metallic wire its length the wire is extended four times its length with uniform width. Then:
- The volume of metal in both the cases is same.
- The surface area of solid wires in both the cases is same.
Which of above statements is/are true?
only 1
only 2
both 1 and 2
neither 1 nor 2
The given figure shows a toy made of very thin metal sheet. The toy has a hemisphere a cylinder and a cone all of the same radius.
Assertion (A): A minimum area of metal sheet required is: Curved surface area of the conical part + curved surface area of the cylinder part − curved surface area of the hemisphere part
Reason (R): Metal sheet required = Curved surface area of (conical part + cylindercal part + hemispherical part)
A is true, R is false.
A is false, R is true.
Both A and R are true and R is the correct reason for A.
Both A and R are true and R is the incorrect reason for A.
The base radii of two right circular cones of the same height are in the ratio 3 : 5.
Assertion (A): The ratio between their volumes is 9 : 25.
Reason (R): As \[\frac{r_{1}}{r_{2}}=\frac{3}{5}\]
\[ \frac{\pi r_{1}^{2} h}{\pi r_{2}^{2} h}=\frac{r_{1}^{2}}{r_{2}^{2}}=\left(\frac{3}{5}\right)^{2}\]
A is true, R is false.
A is false, R is true.
Both A and R are true and R is the correct reason for A.
Both A and R are true and R is the incorrect reason for A.
A solid cone of height 3 cm and radius 3 cm is recast into solid cylinders each of height 1 cm and radius 1 cm.
Assertion (A): Number of cylinders formed \[=\frac{1}{3} \times 3 \times 3 \times 3\]
Reason (R): Number of cylinders formed \[=\frac{\frac{1}{3} \pi(3)^{2} \times 3}{\pi(1)^{2} \times 1}\]
A is true, R is false.
A is false, R is true.
Both A and R are true and R is the correct reason for A.
Both A and R are true and R is the incorrect reason for A.
A solid wooden cylinder is of height h cm and radius r cm. A conical cavity of the same height and the same radius is drilled out of the solid cylinder.
Statement (1): The volume of the remaining wood = volume of solid cylinder − volume of the cone drilled.
Statement (2): Volume of the remaining wood \[= \pi r^2 h - \frac{1}{3}, \pi r^2 h = \frac{2}{3}, \pi r^2 h.\]
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
A solid sphere of radius 6 cm is melted and recast into solid spheres of diameter 2 cm each.
Statement (1): The number of solid spheres formed is 6 × 6 × 6 = 216.
Statement (2): If the smaller spheres formed are identical, the number of solid spheres formed \[=\frac{\text { Volume of sphere melted }}{\text { Volume of each of the sphere formed }}\]
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Water in a canal, 6 m wide and 2 m deep, is flowing with the speed of 18 km/h.
Statement (1): The volume of water that flows through the canal in 20 minutes \[ =6 \times 2 \times\left(18 \times \frac{5}{18}\right) \times 20 \times 60 \mathrm{~m}^{3}\]
Statement (2): The volume of water that flows through the canal = 6 × 2 × 18 × 20 m3.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?
A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere.
A right circular cylinder having diameter 12 cm and height 15 cm is full ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.
A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of π, the volume of the solid.
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
An iron pole consisting of a cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that 1 cm3 of iron has 8 gm of mass (approx). (Take π = `355/113`)
A cylindrical water tank of diameter 2.8 m and height 4.2 m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4 m s–1. Calculate, in minutes, the time it takes to fill the tank.
Water flows, at 9 km per hour, through a cylindrical pipe of cross-sectional area 25 cm2. If this water is collected into a rectangular cistern of dimensions 7.5 m by 5 m by 4 m; calculate the rise in level in the cistern in 1 hour 15 minutes.
The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown.
Calculate :
- the total surface area.
- the total volume of the solid and
- the density of the material if its total weight is 1.7 kg.
A solid, consisting of a right circular cone standing on a hemisphere, is placed upright, in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cubic centimetre.
A metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m.
Calculate:
- the total area of the internal surface, excluding the base;
- the internal volume of the container in m3.
An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85 m and height of the cylindrical part of 50 m. If the diameter of the base is 168 m, find the quantity of canvas required to make the tent. Allow 20% extra for fold and for stitching. Give your answer to the nearest m2.
A test tube consists of a hemisphere and a cylinder of the same radius. The volume of the water required to fill the whole tube is `5159/6 cm^3` and `4235/6 cm^3` of water is required to fill the tube to a level which is 4 cm below the top of the tube. Find the radius of the tube and the length of its cylindrical part.
A solid is in the form of a right circular cone mounted on a hemisphere. The diameter of the base of the cone, which exactly coincides with hemisphere, is 7 cm and its height is 8 cm. The solid is placed in a cylindrical vessel of internal radius 7 cm and height 15 cm. How much water, in cm3, will be required to fill the vessel completely?
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used.
A conical tent is to accommodate 77 persons. Each person must have 16 m3 of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.
A metallic solid cylinder has one end surmounted by a cone of the same radius and a hemisphere, which is also of same radius at that of cone. The conical portion, the cylindercal portion and the hemispherical portion are separated as shown below:
If the radius of the given solid is r cm and the height of the cone = the height of the cylinder = h cm, find expression for the the total surface area of the three parts obtained.
A solid cone of radius 20 cm is cut from its middle, parallel to its base, into two parts as shown. Find:
The ratio between the volumes of the two parts obtained.
Case-Study Based Question
In the given figure, ABCDE represents the bowl of a concrete mixer. ABDE can be a part of a cone FDB as shown below where base radius OD = 30 cm, OP = 20 cm and PF = 1 m.
- Calculate the value of PE using similarity of triangles.
- Calculate the volume of the part with cross-section ABDE.
- Calculate the volume of the whole concrete mixer to the nearest litre.
Solutions for 20: Cylinder, Cone and Sphere
Selina solutions for कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 20 - Cylinder, Cone and Sphere
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Concepts covered in कन्साइस माठेमटिक्स [इंग्रजी] इयत्ता १० आयसीएसई chapter 20 Cylinder, Cone and Sphere are Solid Figures, Mensuration of Cones, Mensuration of a Sphere, Mensuration of Cylinder, Hollow Cylinder, Hemisphere, Conversion of Solids, Problems on Mensuration, Solid Figures, Mensuration of Cones, Mensuration of a Sphere, Mensuration of Cylinder, Hollow Cylinder, Hemisphere, Conversion of Solids, Problems on Mensuration, Solid Figures, Mensuration of Cones, Mensuration of a Sphere, Mensuration of Cylinder, Hollow Cylinder, Hemisphere, Conversion of Solids, Problems on Mensuration.
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