#### Chapters

Chapter 2 - Polynomials

Chapter 3 - Pair of Linear Equations in Two Variables

Chapter 4 - Triangles

Chapter 5 - Trigonometric Ratios

Chapter 6 - Trigonometric Identities

Chapter 7 - Statistics

Chapter 8 - Quadratic Equations

Chapter 9 - Arithmetic Progression

Chapter 10 - Circles

Chapter 11 - Constructions

Chapter 12 - Trigonometry

Chapter 13 - Probability

Chapter 14 - Co-Ordinate Geometry

Chapter 15 - Areas Related to Circles

Chapter 16 - Surface Areas and Volumes

## Chapter 16 - Surface Areas and Volumes

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How many balls each of radius 1cm can be made from a solid sphere of lead of radius

8cm?

How many spherical bullets each of 5cm in diameter can be cast from a rectangular block of metal 11 dm x 1m x 5 dm?

A spherical ball of radius 3cm is melted and recast into three spherical balls. The radii of the two of balls are 19cm and 2cm . Determine the diameter of the third ball?

2.2 Cubic dm of grass is to be drawn into a cylinder wire 0.25cm in diameter. Find the length of wire?

What length of a solid cylinder 2cm in diameter must be taken to recast into a hollow

cylinder of length 16cm, external diameter 20cm and thickness 2.5mm?

A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42cm and height 21cm which are filled completely. Find the diameter of cylindrical vessel?

50 circular plates each of diameter 14cm and thickness 0.5cm are placed one above other to form a right circular cylinder. Find its total surface area?

25 circular plates each of radius 10.5cm and thickness 1.6cm are placed one above the other to form a solid circular cylinder. Find the curved surface area and volume of cylinder so formed?

A path 2m wide surrounds a circular pond of diameter 4cm. how many cubic meters of

gravel are required to grave the path to a depth of 20cm

A 16m deep well with diameter 3.5m is dug up and the earth from it is spread evenly to form a platform 27.5m by 7m. Find height of platform?

A well of diameter 2m is dug14m deep. The earth taken out of it is spread evenly all around it to form an embankment of height 40cm. Find width of the embankment?

Find the volume of the largest right circular cone that can be cut out of a cube where edgeis 9cm_____?

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm. Find the radius and slant height of the heap.

Rain water, which falls on a flat rectangular surface of length 6cm and breath 4m is

transferred into a cylindrical vessel of internal radius 10cm. What will be the height of

water in the cylindrical vessel if a rainfall of 1cm has fallen____?

A conical flask is full of water. The flask has base radius r and height h. the water is proved into a cylindrical flask off base radius one. Find the height of water in the cylindrical flask?

A rectangular tank 15m long and 11m broad is required to receive entire liquid contents from a full cylindrical tank of internal diameter 21m and length 5m. Find least height of tank that will serve purpose______?

A hemisphere tool of internal radius 9cm is full of liquid. This liquid is to be filled into

cylindrical shaped small bottles each of diameter 3cm and height 4cm. how many bottles are necessary to empty the bowl.

The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.

A hollow sphere of internal and external diameter 4cm and 8cm is melted into a cone of base diameter 8cm. Calculate height of cone?

A cylindrical tube of radius 12cm contains water to a depth of 20cm. A spherical ball is dropped into the tube and the level of the water is raised by 6.75cm.Find the radius of the ball___?

500 persons have to dip in a rectangular tank which is 80m long and 50m broad. What is the rise in the level of water in the tank, if the average displacement of water by a person is

0.04m^{3} ____?

A cylindrical jar of radius 6cm contains oil. Iron sphere each of radius 1.5cm are immersed in the oil. How many spheres are necessary to raise level of the oil by two centimetress?

A hollow sphere of internal and external radii 2cm and 4cm is melted into a cone of basse radius 4cm. find the height and slant height of the cone______?

The internal and external diameters of a hollow hemisphere vessel are 21cm and 25.2 cm The cost of painting 1cm^{2 }of the surface is 10paise. Find total cost to paint the vessel all

over______?

A cylindrical tube of radius 12cm contains water to a depth of 20cm. A spherical ball of radius 9cm is dropped into the tube and thus level of water is raised by hcm. What is the value of h_____?

The difference between outer and inner curved surface areas of a hollow right circular cylinder 14cm long is 88cm^{2}. If the volume of metal used in making cylinder is 176cm^{3}.find the outer and inner diameters of the cylinder____?

Prove that the surface area of a sphere is equal to the curved surface area of the circumference cylinder__?

The diameter of a metallic sphere is equal to 9cm. it is melted and drawn into a long wire of diameter 2mm having uniform cross-section. Find the length of the wire?

An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is 1/4 of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.

A tent of height 77dm is in the form a right circular cylinder of diameter 36m and height 44dm surmounted by a right circular cone. Find the cost of canvas at Rs.3.50 per 2 m ?

Metal spheres each of radius 2cm are packed into a rectangular box of internal dimension 16cm x 8cm x 8cm when 16 spheres are packed the box is filled with preservative liquid. Find volume of this liquid?

The largest sphere is to be curved out of a right circular of radius 7cm and height 14cm. find volume of sphere?

A copper sphere of radius 3cm is melted and recast into a right circular cone of height 3cm.find radius of base of cone?

A vessel in the shape of cuboid ontains some water. If these identical spheres are immersed in the water, the level of water is increased by 2cm. if the area of base of cuboid is 160cm^{2} and its height 12cm, determine radius of any of spheres?

A copper rod of diameter 1cm and length 8cm is drawn into a wire of length 18m of uniform thickness. Find thickness of wire?

The diameters of internal and external surfaces of hollow spherical shell are 10cm and 6cm respectively. If it is melted and recast into a solid cylinder of length of 2`2/3`cm, find the

diameter of the cylinder.

A right angled triangle whose sides are 3 cm, 4 cm and 5 cm is revolved about the sides containing the right angle in two days. Find the difference in columes of the two cones so formed. Also, find their curved surfaces.

How many coins 1.75cm in diameter and 2mm thick must be melted to form a cuboid 11cm x 10cm x 75cm___?

A well with inner radius 4m is dug 14m deep earth taken out of it has been spread evenly all around a width of 3m it to form an embankment. Find the height of the embankment?

Water in a canal 1.5m wide and 6m deep is flowering with a speed of 10km/ hr. how much area will it irrigate in 30 minutes if 8cm of standing water is desired?

A farmer runs a pipe of internal diameter 20 cm from the canal into a cylindrical tank in his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of height 28 cm. Find the diameter of the base of the cone so formed (Use it =`22/7`)

The volume of a hemisphere is 2425`1/2cm^3`cm. Find its curved surface area?

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A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of canvas required for the tent.

A rocket is in the form of a circular cylinder closed at the lower end with a cone of the same radius attached to the top. The cylinder is of radius 2.5m and height 21m and the cone has a slant height 8m. Calculate total surface area and volume of the rocket?

A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?

A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use n =`22/7`)

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively.The radii of the hemispherical and conical parts are the same as that of the cylindrical part.Find the surface area of the toy if the total height of the toy is 30 cm.

A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the hemisphere is immersed in the tub. If the radius of the hemi-sphere is 3.5 cm and height of the cone outside the hemisphere is 5 cm, find the volume of the water left in the tub (Take π = 22/7)

A circus tent has cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is 20 m. The heights of the cylindrical and conical portions are 4.2 m and 2.1 m respectively. Find the volume of the tent.

A petrol tank is a cylinder of base diameter 21 cm and length 18 cm fitted with conical ends each of axis length 9 cm. Determine the capacity of the tank.

A conical hole is drilled in a circular cylinder of height 12 cm and base radius 5 cm. The height and the base radius of the cone are also the same. Find the whole surface and volume of the remaining cylinder.

A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. Find the capacity of the tent and the cost of the canvas at Rs 100 per square metre.

A boiler is in the form of a cylinder 2 m long with hemispherical ends each of 2 metre diameter. Find the volume of the boiler.

A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is `14/3` m and the diameter of hemisphere is 3.5 m. Calculate the volume and the internal surface area of the solid.

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each of the hemispherical ends is 7 cm, find the cost of polishing its surface at the rate of Rs 10 per dm^{2} .

A cylindrical vessel of diameter 14cm and height 42cm is fixed symmetrically inside a similar vessel of diameter 16cm and height 42 . cm The total space between two vessels is filled with cork dust for heat insulation purpose. How many cubic cms of cork dust will be

required?

A cylindrical road roller made of iron is 1 m long, Its internal diameter is 54 cm and the thickness of the iron sheet used in making the roller is 9 cm. Find the mass of the roller, if 1 cm^{3} of iron has 7.8 gm mass. (Use π = 3.14)

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. [Use π = 22/7]

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy [Use π =22/7]

The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m^{2}. If the pipe is made of 99 cm^{3} of metal, find the outer and inner radii of the pipe.

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 iron pole having 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 the mass of 1 cm^{3}of iron is 8 gm.

A solid toy is in the form of a hemisphere surmounted by a right circular cone. height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find how much more space it will cover.

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm. Use [Π = 22/7]

A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the value of water (i) displaced out of the cylinder (ii) left in the cylinder. (Take π 22/7)

A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Determine the volume and total surface area of the remaining block.

A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is `2/3` of the volume of hemisphere, calculate the height of the cone and the surface area of the toy.

`(use pi = 22/7)`

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them is being 3.5 cm and the total height of solid is 9.5 cm. Find the volume of the solid. (Use π = 22/7).

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A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm^{2 }. (Use π = 3.14)

A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. find the curved surface area of the frustum.

The perimeters of the ends of a frustum of a right circular cone are 44 cm and 33 cm. If the height of the frustum be 16 cm, find its volume, the slant surface and the total surface.

If the radii of the circular ends of a conical bucket which is 45 cm high be 28 cm and 7 cm, find the capacity of the bucket. (Use π = 22/7).

The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.

If the radii of circular ends of a bucket 24cm high are 5cm and 15cm. find surface area of

bucket?

The radii of the circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.

A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13 m and 7 m , the height of the frustum be 8 m and the slant height of the conical cap be 12 m, find the canvas required for the tent. (Take : π = 22/7)

A reservoir in the form of the frustum of a right circular cone contains 44 × 10^{7} litres of water which fills it completely. The radii of the bottom and top of the reservoir are 50 metres and 100 metres respectively. Find the depth of water and the lateral surface area of the reservoir. (Take: π = 22/7)

A metallic right circular cone 20cm high and whose vertical angle is 90° is cut into two parts at the middle point of its axis by a plane parallel to base. If frustum so obtained bee

drawn into a wire of diameter

(1/16) cm find length of the wire?

A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm^{3} of water.The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of the metal sheet used in its making. (Use 𝜋 = 3.14).

A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per

100 cm^{2}

Radii of circular ends of a solid frustum off a cone re 33cm and 27cm and its slant height are 10cm. find its total surface area?

A bucket made up of a metal sheet is in form of a frustum of cone of height 16cm with diameters of its lower and upper ends as 16cm and 40cm. find the volume of bucket. Also find cost of bucket if the cost of metal sheet used is Rs 20 per 100 cm^{2}

A solid is in the shape of a frustum of a cone. The diameter of two circular ends are 60cm and 36cm and height is 9cm. find area of its whole surface and volume?

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 `3/7` cm^{3}. The radii of its lower and upper circular ends are 8cm and 20cm. find the cost of metal sheet used in making container at rate of Rs 1.4 per cm^{2}?

#### Textbook solutions for Class 10

## R.D. Sharma solutions for Class 10 Mathematics chapter 16 - Surface Areas and Volumes

R.D. Sharma solutions for Class 10 Mathematics chapter 16 (Surface Areas and Volumes) include all questions with solution and detail explanation from 10 Mathematics. 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 created the CBSE 10 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10 Mathematics chapter 16 Surface Areas and Volumes are Volume of a Combination of Solids, Surface Area of a Combination of Solids, Conversion of Solid from One Shape to Another, Frustum of a Cone, Introduction of Surface Areas and Volumes, Surface Areas and Volumes Examples and Solutions.

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