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RD Chapter 21 Surface Areas and Volume of a Sphere Ex VSAQS Solutions

Question - 1 : - Find the surface area of a sphere of radius 14 cm.

Answer - 1 : -

Radiusof a sphere (r) = 14 cm
∴Surface area = 4πr2 = 4 x x 14 x 14 cm2

= 2464 cm3

Question - 2 : - Find the total surface afea of a hemisphere of radius 10 cm.

Answer - 2 : -

Radius of hemisphere (r) = 10 cm
∴ Total surface area = 3πr2

Question - 3 : - Find the radius of a sphere whose surface area is 154 cm2.

Answer - 3 : - Surface area of a sphere = 154 cm2

Question - 4 : - The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motor cyclist for riding.

Answer - 4 : - Diameter of hollow sphere = 7 m

Question - 5 : - Find the volume of a sphere whose surface area is 154 cm2.

Answer - 5 : - Surface area of a sphere = 154 cm2

Question - 6 : - 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?

Answer - 6 : - Edge of a solid cube = 44 cm
∴ Volume = a2 =(44)2 cm2
= 44 × 44 × 44 cm3
Diameter of a spherical bullet = 4 cm

Question - 7 : - 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.

Answer - 7 : - Radius of a sphere (R) = 2r

Question - 8 : - If a hollow sphere of intefnal 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.

Answer - 8 : - Internal diameter of a hollow sphere = 4cm
∴ Internal radius = 4/2 = 2 cm
Similarly the outer radius (R) = 8/2 = 4 cm
∴ Volume of melted used inhollow sphere

Question - 9 : - 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.

Answer - 9 : - Radius of a sphere (r) = 5 cm
∴ Surface area = 4πr2
= 4π x 5 x 5 = 100π cm2
Radius of cone (r1) = 4 cm

Question - 10 : - If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.

Answer - 10 : - Let edge of a cube = a
Then its volume = a3
∵ A sphere is inscribed inthe cube
∴ Diameter of sphere = a

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