Q. 213.6( 20 Votes )

# A solid is in the

A solid is in the form of a right circular cone mounted on a hemisphere.

Let r be the radius of hemisphere and cone

Let h be the height of the cone

Radius of hemisphere = r = 2.1 cm

Volume of hemisphere = 2/3 πr3

= 2/3 × 22/7 × 2.1 × 2.1 × 2.1 cm3

= 19.404 cm3

Height of cone = h = 4 cm

Radius of cone = r = 2.1 cm

Volume of cone = 1/3 πr2h

= 1/3 × 22/7 × 2.1 × 2.1 × 4 cm3

= 18.48 cm3

Volume of solid = Volume of hemisphere + Volume of cone

= 19.404 cm3 + 18.48 cm3 = 37.884 cm3

The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water, so, to find the volume of water left in the tub we need to subtract volume of solid from cylindrical tub.

Radius of cylinder = r’ = 5 cm

Height of cylinder = h’ = 9.8 cm

Volume of cylindrical tub = πr’2h’ = 22/7 × 5 × 5 × 9.8 cm3

= 770 cm3

Volume of water left in the tub = Volume of cylindrical tub – Volume of solid

Volume of water left in the tub = 770 cm3 – 37.884 cm3 = 732.116 cm3

Volume of water left in the tub is 732.116 cm3

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