RD SHARMA SOLUTION CHAPTER -21 Surface Area and Volume of a Sphere| CLASS 9TH MATHEMATICS-EDUGROWN

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

Question 1

Solution 1

Question 2

Solution 2

Question 3

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Question 4

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Question 5A 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

Question 6

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Question 7

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Question 8

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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

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

Question 11

Solution 11

Question 12

Solution 12

Question 13The 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. 

                                      Solution 13

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

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9If 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

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

Question 11

Solution 11

Question 12

Solution 12

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

Question 14

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Question 15

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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

Question 17

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Question 18

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Question 19

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Question 20

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Question 21

A cube of side 4 cm contained a sphere touching its sides. Find the volume of the gap in between.Solution 21

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 22Inner 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 mVolume of iron used to make the tank  = 

                                                            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 23Radius (r) of capsule
Volume of spherical capsule

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 be  .
    Then, diameter of moon will be  . So, radius of moon will be  .
    Volume of moon =    
    Volume of earth =   

    Thus, the volume of moon is  of volume of earth.

Question 25

Solution 25

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

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  = 22/7)Solution 27

Question 28

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Question 29

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Question 30

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Question 31

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Question 32

Solution 32