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RD Chapter 21 Surface Areas and Volume of a Sphere Ex 21.2 Solutions

Question - 1 : -
Find the volume of a sphere whose radius is
(i) 2 cm
(ii) 3.5 cm
(iii) 10.5 cm

Answer - 1 : - (i) Radius of sphere (r) = 2 cm

Question - 2 : -
Find the volume of a sphere whose diameter is,
(i) 14 cm
(ii) 3.5 dm
(iii) 2.1 m

Answer - 2 : - (i) Diameter of a sphere = 14 cm

Question - 3 : - A hemspherical tank has inner radius of 2.8 m. Find its capacity in litres.

Answer - 3 : - Radius of hemispherical tank (r) = 2.8 m

Question - 4 : - 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.

Answer - 4 : - Thickness of steel = 0.25 cm = 1/4cm
Inside radius of the hemispherical bowl (r) = 5 cm
∴ Outer radius (R) = 5 +0.25 = 5.25 cm
∴ Volume of the steel used= π(R3 – r3)


Question - 5 : - How many bullets can be made out of a cube of lead,whose edge measures 22 cm, each bullet being 2 cm in diameter?

Answer - 5 : - Edge of cube (r) = 22 cm
∴ Volume = a3 =(22)3 cm3
= 22 x 22 x 22 = 10648 cm3
Diameter of a bullet = 2 cm

Question - 6 : - A shopkeeper has one laddoo of radius 5 cm. With the same material how many laddoos of radius 2.5 cm can be made?

Answer - 6 : - Radius of bigger laddoo (R) = 5 cm

Question - 7 : - A spherical ball of lead 3 cm in diameter is melted and recast into three spherical balls. It the diameters of two balls be 3/2 cm and 2 cm, find the diameter of the third ball.

Answer - 7 : - Diameter of a spherical ball of lead = 3 cm

Question - 8 : - A sphere of radius 5 cm is immersed in water filled in a cylinder, the level of water rises 5/3 cm. Find the radius of the cylinder.

Answer - 8 : - Radius of sphere (r1) = 5 cm

Level of water rises in the cylinder after immersing the sphere in it
∴ Height of water level = 5/3 cm
Let r be radius of the cylinder, then Volume of water = Volume of the sphere

Question - 9 : - If the radius of a sphere is doubled, what is the ratio of the volumes of the first sphere to that of the second sphere?

Answer - 9 : -

Let r2 be the radius of the given sphere
then volume =πr3
By doubling the radius the radius of the new sphere = 2r

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.

Answer - 10 : - Radius of hemispherical bowl (r) = 3.5 cm

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