# RD Sharma solutions for Mathematics for Class 9 chapter 21 - Surface Areas and Volume of a Sphere [Latest edition]

#### Chapters ## Chapter 21: Surface Areas and Volume of a Sphere

Exercise 21.1Exercise 21.2Others
Exercise 21.1 [Pages 8 - 9]

### RD Sharma solutions for Mathematics for Class 9 Chapter 21 Surface Areas and Volume of a SphereExercise 21.1 [Pages 8 - 9]

Exercise 21.1 | Q 1.1 | Page 8

Find the surface area of a sphere of radius 10.5 cm .

Exercise 21.1 | Q 1.2 | Page 8

Find the surface area of a sphere of radius 5.6 cm .

Exercise 21.1 | Q 1.3 | Page 8

Find the surface area of a sphere of radius 14 cm .

Exercise 21.1 | Q 2.1 | Page 8

Find the surface area of a sphere of diameter 14 cm .

Exercise 21.1 | Q 2.2 | Page 8

Find the surface area of a sphere of diameter 21 cm .

Exercise 21.1 | Q 2.3 | Page 8

Find the surface area of a sphere of diameter 3.5 cm .

Exercise 21.1 | Q 3 | Page 8

Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use 𝜋 = 3.14)

Exercise 21.1 | Q 4 | Page 8

The surface area of a sphere is 5544 cm^2, find its diameter.

Exercise 21.1 | Q 5 | Page 8

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin- plating
it on the inside at the rate of Rs. 4 per 100 cm^2

Exercise 21.1 | Q 6 | Page 8

The dome of a building is in the form of a hemisphere. Its radius is 63 dm. Find the cost of
painting it at the rate of Rs. 2 per sq. m.

Exercise 21.1 | Q 7 | Page 8

Assuming the earth to be a sphere of radius 6370 km, how many square kilo metres is area
of the land, if three-fourth of the earth’s surface is covered by water?

Exercise 21.1 | Q 8 | Page 8

A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 cm.

Exercise 21.1 | Q 9 | Page 8

The diameter of the moon is approximately one fourth of the diameter of the earth. Find the
ratio of their surface areas.

Exercise 21.1 | Q 10 | Page 8

A hemi-spherical dome of a building needs to be painted. If the circumference of the base of
the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs. 5 per l00
cm^2

Exercise 21.1 | Q 11 | Page 8

A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base
of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100
cm^2.

Exercise 21.1 | Q 12 | Page 8

A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the
external diameter of the cylinder be 1.4 m and its length be 8 m, find the cost of painting it
on the outside at the rate of Rs. 10 per m^2.

Exercise 21.1 | Q 13 | Page 9

The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm2 and black paint costs 5 paise per cm2. Exercise 21.2 [Pages 20 - 22]

### RD Sharma solutions for Mathematics for Class 9 Chapter 21 Surface Areas and Volume of a SphereExercise 21.2 [Pages 20 - 22]

Exercise 21.2 | Q 1.1 | Page 20

Find the volume of a sphere whose radius is 2 cm.

Exercise 21.2 | Q 1.2 | Page 20

Find the volume of a sphere whose radius is 3.5 cm.

Exercise 21.2 | Q 1.3 | Page 20

Find the volume of a sphere whose radius is 10.5 cm .

Exercise 21.2 | Q 2.1 | Page 20

Find the volume of a sphere whose diameter is 14 cm .

Exercise 21.2 | Q 2.2 | Page 20

Find the volume of a sphere whose diameter is 3.5 dm .

Exercise 21.2 | Q 2.3 | Page 20

Find the volume of a sphere whose diameter is 2.1 m .

Exercise 21.2 | Q 3 | Page 20

A hemispherical tank has inner radius of 2.8 m. Find its capacity in litres.

Exercise 21.2 | Q 4 | Page 20

A hemispherical bowl is made of steel 0.25 cm thick. The inside radius of the bowl is 5 cm. Find the volume of steel used in making the bowl.

Exercise 21.2 | Q 5 | Page 20

How mañy bullets can be made out of a cube of lead, whose edge measures 22 cm, each bullet being 2 cm in diameter?

Exercise 21.2 | Q 6 | Page 20

Exercise 21.2 | Q 7 | Page 20

A spherical ball of lead 3 cm in diameter is melted and recast into three spherical balls. If the diameters of two balls be 3/2cm and 2 cm, find the diameter of the third ball.

Exercise 21.2 | Q 8 | Page 20

A sphere of radius 5 cm is immersed in water filled in a cylinder, the level of water rises 5/3cm. Find the radius of the cylinder.

Exercise 21.2 | Q 9 | Page 20

If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere?

Exercise 21.2 | Q 10 | Page 20

A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which the water will rise in the cylinder.

Exercise 21.2 | Q 11 | Page 20

A cylinder whose height is two thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.

Exercise 21.2 | Q 12 | Page 20

A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively 6 cm and 4 cm. Find the height of water in the cylinder

Exercise 21.2 | Q 13 | Page 21

The diameter of a coper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, find its diameter.

Exercise 21.2 | Q 14 | Page 21

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.

Exercise 21.2 | Q 15 | Page 21

The radius of the internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. If it is melted and recast into a solid cylinder of heigh22/3cm Find the diameter of the cylinder.

Exercise 21.2 | Q 16 | Page 21

A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find the radius of the base.

Exercise 21.2 | Q 17 | Page 21

A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone.

Exercise 21.2 | Q 18 | Page 21

A metallic sphere of radius 10.5 cm is melted and thus recast into small cones, each of radius 3.5 cm and height 3 cm. Find how many cones are obtained.

Exercise 21.2 | Q 19 | Page 21

A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

Exercise 21.2 | Q 20 | Page 21

The largest sphere is carved out of a cube of side 10.5 cm. Find the volume of the sphere.

Exercise 21.2 | Q 21 | Page 21

A cube of side 4 cm contains a sphere touching its side. Find the volume of the gap in between.

Exercise 21.2 | Q 22 | Page 21

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.

Exercise 21.2 | Q 23 | Page 21

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine ("in " mm^3) is needed to fill this capsule?

Exercise 21.2 | Q 24 | Page 21

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

Exercise 21.2 | Q 25 | Page 21

A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.

Exercise 21.2 | Q 26 | Page 21

A cylindrical tub of radius 16 cm contains water to a depth of 30 cm. A spherical iron ball is dropped into the tub and thus level of water is raised by 9 cm. What is the radius of the ball?

Exercise 21.2 | Q 27 | Page 21

A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball.
(Use 𝜋 = 22/7).

Exercise 21.2 | Q 28 | Page 21

A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1 .5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimetres?

Exercise 21.2 | Q 29 | Page 21

A measuring jar of internal diameter 10 cm is partially filled with water. Four equal spherical balls of diameter 2 cm each are dropped in it and they sink down in water completely. What will be the change in the level of water in the jar?

Exercise 21.2 | Q 30 | Page 21

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.

Exercise 21.2 | Q 31 | Page 22

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?

Exercise 21.2 | Q 32 | Page 22

A sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. Find the ratio of their volumes.

[Pages 25 - 26]

### RD Sharma solutions for Mathematics for Class 9 Chapter 21 Surface Areas and Volume of a Sphere [Pages 25 - 26]

Q 1 | Page 25

Find the surface area of a sphere of radius 14 cm.

Q 2 | Page 25

Find the total surface area of a hemisphere of radius 10 cm.

Q 3 | Page 25

Find the radius of a sphere whose surface area is 154 cm2.

Q 4 | Page 25

The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.

Q 5 | Page 25

Find the volume of a sphere whose surface area is 154 cm2.

Q 6 | Page 25

How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?

Q 7 | Page 26

If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.

Q 8 | Page 25

If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.

Q 9 | Page 25

The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.

Q 10 | Page 25

If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.

[Pages 25 - 27]

### RD Sharma solutions for Mathematics for Class 9 Chapter 21 Surface Areas and Volume of a Sphere [Pages 25 - 27]

Q 1 | Page 25

Mark the correct alternative in each of the following:
In a sphere the number of faces is

• 1

• 2

• 3

• 4

Q 2 | Page 25

The total surface area of a hemisphere of radius r is

• $\pi r^2$

• 2 $\pi r^2$

• 3 $\pi r^2$

• 4 $\pi r^2$

Q 3 | Page 25

The ratio of the total surface area of a sphere and a hemisphere of same radius is

• 2 : 1

• 3 : 2

•  4 : 1

• 4 : 3

Q 4 | Page 25

A sphere and a cube are of the same height. The ratio of their volumes is

• 3 : 4

•  21 : 11

• 4 : 3

• 11 : 21

Q 5 | Page 25

The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be

• 27 $\pi$ cm3

• 36 $\pi$ cm3

• 108 $\pi$ cm3

• 12 $\pi$ cm3

Q 6 | Page 26

A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be

• 4

• 3

• 6

• 8

Q 7 | Page 26

If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is

• 1 : 2

• 1 : 4

• 1 : 8

• 1 : 16

Q 8 | Page 26

If the surface area of a sphere is 144π m2, then its volume (in m3) is

• 288 π

• 316 π

• 300 π

• 188 π

Q 9 | Page 26

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is

• 100 π

• 75 π

• 60 π

• 50 π

Q 10 | Page 27

If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is

•  π : 2

•  π : 3

• π : 4

• π : 6

Q 11 | Page 27

If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is

• 2r

• 3r

• r

• 4r

Q 12 | Page 27

A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is

•  4πr3

• 8/3 pi r^3

•  2πr3

•  8πr3

Q 13 | Page 27

The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is

• 2 : 1

• 1 : 1

•  2 : 3

•  1 : 2

Q 14 | Page 27

A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is

• 1 : 2

•  2 : 1

• 4 : 1

• $\sqrt{2}$ : 1

Q 15 | Page 27

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is

• 1 : 2 : 3

•  2 : 1 : 3

•  2 : 3 : 1

• 3 : 2 : 1

## Chapter 21: Surface Areas and Volume of a Sphere

Exercise 21.1Exercise 21.2Others ## RD Sharma solutions for Mathematics for Class 9 chapter 21 - Surface Areas and Volume of a Sphere

RD Sharma solutions for Mathematics for Class 9 chapter 21 (Surface Areas and Volume of a 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 CBSE Mathematics for Class 9 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics for Class 9 chapter 21 Surface Areas and Volume of a Sphere are Surface Area of a Sphere, Volume of a Cuboid, Volume of a Cylinder, Volume of a Right Circular Cone, Volume of a Sphere, Surface Area of a Cuboid, Surface Area of Cylinder, Surface Area of a Right Circular Cone.

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