Q. 29 4.0( 3 Votes )

A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the volume of wood in the toy.

Answer :

Given height of cylinder = h = 10 cm

Radius of cylinder = r = 3.5 cm

Radius of hemisphere = R = 3.5 cm

Explanation: In this question the volume of wood in toy can be calculated by subtracting the volume of two hemisphere from the volume of cylinder.

So, volume of cylinder = πr2h

Where r = radius of cylinder and h = height of cylinder

Volume of cylinder = π × (3.5)2 × 10 (from given values)

Volume of cylinder = π × 12.25 × 10

Volume of cylinder = 122.5π cm3eqn1

Volume of a hemisphere(where R is radius of hemisphere)

Volume of two hemisphere

Volume of wood in toy = eqn1 – eqn2

Volume of wood in toy

(taking π common)

Volume of wood in toy = 205.333 cm3

Volume of wood in toy is 205.333 cm3.

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