RD SHARMA Solutions for Class 9 Maths Chapter 21 - Surface Areas and Volume of a Sphere

Revise RD Sharma Solutions for CBSE Class 9 Maths Chapter 21 Surface Areas and Volume of a Sphere at TopperLearning. Understand the steps to find the surface area of a sphere based on information about its diameter. Learn to use the correct formula to find the total surface area of a given solid hemisphere or the volume of a sphere.

The concepts covered in this CBSE Class 9 Maths chapter are important. These concepts form the foundation of Maths knowledge required for solving complex problems in higher classes. Ensure conceptual clarity in Class 9 with our online education portal’s videos, test materials and other Mathematics resources.

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Chapter 21 - Surface Areas and Volume of a Sphere Exercise Ex. 21.1

Question 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 5
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 cm2.
Solution 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 9

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

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 10

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, if given the cost of painting is Rs 5 per 100 cm2.

Solution 10


Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 13
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.
 
                                       Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 13
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Chapter 21 - Surface Areas and Volume of A Sphere Exercise Ex. 21.2

Question 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Solution 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 9
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?
Solution 9
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 10

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.

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 13

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.

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 16

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.

Solution 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 21

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

Solution 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 22

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.

Solution 22
Inner radius (r1) of hemispherical tank  = 1 m
     Thickness of hemispherical tank       = 1 cm = 0.01 m
Outer radius (r2) of hemispherical tank = (1 + 0.01) m = 1.01 m
Volume of iron used to make the tank  = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
                                                            Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Question 23

A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm3) is needed to fill this capsule?

Solution 23
Radius (r) of capsuleRd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere  
Volume of spherical capsuleRd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
                                        Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
Thus, approximately 22.46 mm3 of medicine is required to fill the capsule.

Question 24

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?

Solution 24
    Let diameter of earth be d. So, radius earth will beRd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere  .
    Then, diameter of moon will be Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere . So, radius of moon will be Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere .
    Volume of moon =    Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
    Volume of earth =   Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
      Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere
    Thus, the volume of moon is Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere of volume of earth.

Question 25

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 25

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 26

A cylinderical 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?

Solution 26

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 27

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 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere = 22/7)

Solution 27

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 28

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 28

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 29

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 29

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 30

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 30

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 31

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 31

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 32

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 32

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Chapter 21 - Surface Areas and Volume of a Sphere Exercise 21.26

Question 1

In a sphere the number of faces is

(a) 1

(b) 2

(c) 3

(d) 4

Solution 1

Sphere has only one surface i.e. curved surface, so number of faces = 1

Hence, correct option is (a).

Question 2

The total surface area of a hemisphere of radius r is

(a) ∏r2

(b) 2∏r2

(c) 3∏r2

(d) 4∏r2

Solution 2

A hemisphere has two surfaces: one top surface and other curved surface.

T.S.A. = 2∏r2 + (∏r2)   {Area of Top-face = ∏r2}

         = 3∏r2

Question 3

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

(a) 2 : 1

(b) 3 : 2

(c) 4 : 1

(d) 4 : 3

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 4

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

(a) 3 : 4

(b) 21 : 11

(c) 4 : 3

(d) 11 : 21

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 5

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

(a) 27∏ cm3

(b) 36∏ cm3

(c) 108∏ cm3

(d) 12∏ cm3

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 6

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

(a) 4

(b) 3

(c) 6

(d) 8

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 7

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

(a) 1 : 2

(b) 1 : 4

(c) 1 : 8

(d) 1 : 16

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 8

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

(a) 288 ∏

(b) 316 ∏

(c) 300 ∏

(d) 188 ∏

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 9

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

(a) 100∏

(b) 75∏

(c) 60∏

(d) 50∏

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Chapter 21 - Surface Areas and Volume of a Sphere Exercise 21.27

Question 10

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

(a) ∏ : 2

(b) ∏ : 3

(c) ∏ : 4

(d) ∏ : 6

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 11

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

(a) 2r

(b) 3r

(c) r

(d) 4r

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Radius of sphere = r

Sphere touches cylinder at Top, Base and Lateral Surface.

Then,

2r = height of cylinder = h

r = Radius of cylinder

Volume of cylinder = ∏r2h

                         =∏r2(2r)

                         = 2∏r3

Hence, correct option is (c).


Question 13

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

(a) 2 : 1

(b) 1 : 1

(c) 2 : 3

(d) 1 : 2

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Question 15

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

(a) 1 : 2 : 3

(b) 2 : 1 : 3

(c) 2 : 3 : 1

(d) 3 : 2 : 1

Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Sphere