#### Chapters

Chapter 2: Banking (Recurring Deposit Account)

Chapter 3: Shares and Dividend

Chapter 4: Linear Inequations (In one variable)

Chapter 5: Quadratic Equations

Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)

Chapter 7: Ratio and Proportion (Including Properties and Uses)

Chapter 8: Remainder and Factor Theorems

Chapter 9: Matrices

Chapter 10: Arithmetic Progression

Chapter 11: Geometric Progression

Chapter 12: Reflection

Chapter 13: Section and Mid-Point Formula

Chapter 14: Equation of a Line

Chapter 15: Similarity (With Applications to Maps and Models)

Chapter 16: Loci (Locus and Its Constructions)

Chapter 17: Circles

Chapter 18: Tangents and Intersecting Chords

Chapter 19: Constructions (Circles)

Chapter 20: Cylinder, Cone and Sphere

Chapter 21: Trigonometrical Identities

Chapter 22: Height and Distances

Chapter 23: Graphical Representation

Chapter 24: Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Chapter 25: Probability

#### Selina Selina ICSE Concise Mathematics Class 10

## Chapter 20: Cylinder, Cone and Sphere

#### Chapter 20: Cylinder, Cone and Sphere solutions [Page 0]

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 height of the cone (Take π = 3.14)

Two right circular cone x and y are made x having three times the radius of y and y having half the volume of x. Calculate the ratio between the heights of x and y.

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?

Find what length of canvas, 1.5 m in width, is required to make a conical tent 48 m in diameter and 7 m in height. Given that 10% of the canvas is used in folds and stitching’s. Also. Find the cost of the canvas at the rate of Rs. 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:

(i) its radius in cm

(ii) 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 curved surface area of the solid.

A vessel, in the form of an inverted cone, is filled with water to 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 is volume of each of the solid cone submerged?

The volume of a conical tent is 1232 m3 and the area of the base floor is 154 m2. Calculate the:

(i) radius of the floor.

(ii) height of the tent

(iii) length of the canvas required to cover this conical tent if its width is 2 m.

#### Chapter 20: Cylinder, Cone and Sphere solutions [Page 0]

The surface area of a sphere is `2464 cm^2`, find its volume

The volume of a sphere is `38808 cm^3`; 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?

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.

How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm.

Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.

The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their:

(i) radii (ii) 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:

(i) internal curved surface area

(ii) external curved surface area

(iii) total surface area

(iv) 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 re casted into a single solid sphere. Taking π = 3.1, find the surface area of solid sphere formed.

The surface area of a solid sphere is increased by 12% without changing its shape. Find the

percentage increase in its:

(i) radius (ii) volume

#### Chapter 20: Cylinder, Cone and Sphere solutions [Page 0]

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 surface of a metallic spherical. 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 container each of diameter 3 cm and height 4 cm. How many container are necessary to empty the bowl?

A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into a inverted cone of radius 4.8 cm. Find the height of the cone is it is completely filled.

A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5cm. Find the number of sphere formed.

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:

(i) the radius of the solid sphere

(ii) the number of cones recast

A solid metallic cone, with radius 6 cm and height 10cm, is made of some heavy metal A. In order to reduce its weight, a conical hole is made in the cone as shown and it is completely filled with a lighter metal B. The conical hole has a diameter of cm and depth 4 cm calculate the ratio of the volume of metal A to the volume of the metal B in the solid.

A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and react into small cones of base radius 2 cm and height 8 cm. Find the number of cones.

#### Chapter 20: Cylinder, Cone and Sphere solutions [Page 0]

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:

(i) the surface area of remaining solid,

(ii) the volume of remaining solid

(iii) the weight of the material drilled out if it weighs 7 gm per `cm^3`.

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. If is filled with water up to the rim. 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 sopped 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 area melted and recast into a solid sphere of radius R. Find the height of each cone in terms r1, r2 and R.

A solid metallic hemisphere of diameter 28 cm is melted and recast into a number of identical solid cones, each of diameter 14 cm and height 8 cm. find the number of cones so formed.

A cone and hemisphere have the same base and the same height. Find the ratio between their volumes.

#### Chapter 20: Cylinder, Cone and Sphere solutions [Page 0]

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 8m surmounted by a conical part. If total height of the tent is 13m and the diameter of its base is 24m; calculate:

(i) total surface area of the tent,

(ii) area of canvas, required to make this tent allowing 10% of the canvas used for folds and stitching.

A cylindrical boiler, 2 m high, is 3.5 m in diameter. It has a hemispherical lid. Find the volume of its interior, including the part covered by the lid.

A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is `4 2/3` m and the diameter of hemisphere is 3.5 m. Calculate the capacity and the internal surface area of the vessel.

A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside. If the height of the cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone = twice the radius of the base of the cylinder = 10 cm; find the total surface area of the toy.

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 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.

The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per `m^2`.

The horizontal cross-section of a water tank is in the shape of a rectangle with semi-circle at one end, as shown in the following figure. The water is 2.4 metres deep in the tank. Calculate the volume of water in the tank in gallons.

The given figure shows the cross section of a water channel consisting of a rectangle and a semicircle. Assuming that the channel is always full, find the volume of water discharged through it in one minute if water is flowing at the rate of 20 cm per second. Give your answer in cubic metres correct to one place of decimal.

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:

(i) the total surface area of the can in contact with water when the sphere is in it;

(ii) 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.

#### Chapter 20: Cylinder, Cone and Sphere solutions [Page 0]

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 one 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).

In the following diagram a rectangular platform with a semi-circular end on one side is 22 metres long from one end to the other end. If the length of the half circumference is 11 metres. Find the cost of constructing the platform, 1.5 metres high at the rate of Rs. 4 per cubic metres.

The cross-section of a tunnel is a square of side 7m surmounted by a semi circle as shown in the adjoining figure. The tunnel is 80 m long.

(1) its volume

(2) the surface area of the tunnel (excluding the floor) and

(3) its floor area.

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 rater 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 therise in level in the cistern in 1 hour 15 minutes.

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 imensions 7.5 m by 5 m by 4 m; calculate therise in level in the cistern in 1 hour 15 minutes.

Calculate:

(a) the total surface area,

(b) the total volume of the solid and

(c) the density of the material if its total weight is 1.7 kg..

A solid, consisting of a right circular cone standing one 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 cone is 4 cm. Give your answer to the nearest cubic centimeter.

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:

(i) the total area of the internal surface, excluding the base;

(ii) 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 `m^2`

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 ccm^3` and `4235/6 cm^3` cm3 of water is required to fill the tube to a level which is 4 cm below the top of the tune. 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 10 cm. How much water, in cm3, will be required to fill the vessel completely.

## Chapter 20: Cylinder, Cone and Sphere

#### Selina Selina ICSE Concise Mathematics Class 10

#### Textbook solutions for Class 10

## Selina solutions for Class 10 Mathematics chapter 20 - Cylinder, Cone and Sphere

Selina solutions for Class 10 Maths chapter 20 (Cylinder, Cone and Sphere) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Selina ICSE Concise Mathematics for Class 10 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 20 Cylinder, Cone and Sphere are Volume of a Combination of Solids, Perimeter and Area of a Circle, Area and Volume of Solids - Cone, Area and Volume of Solids - Sphere, Circle - Direct Application Problems Including Inner and Outer Area, Three-dimensional Solids Right Circular Cone, Three-dimensional Solids Sphere, Volume of a Cylinder.

Using Selina Class 10 solutions Cylinder, Cone and Sphere exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Selina Textbook Solutions to score more in exam.

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