Mensuration-57

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A solid is in the form of a circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm
and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water, in such a way that the
whole solid is submerged in water. If the radius of the cylinder is 5 cm and its height is 9.8 cm.
find the volume of water left in the cylindrical tub.

Solution: Height of the cylinder = H = 9.8 cm

Radius of cylindrical tub = R = 5 cm

Volume of water in cylindrical tub = Π R2 H

= (Π x 5 x 5 x 9.8) cm2

= (22/7 x 25 x 98/10) cm2

Radius of hemisphere = Radius of cone = r = 2.1 cm

Height of conical portion = 4 cm

Therefore, Volume of solid = Volume of hemisphere + Volume of cone

= 2/3 Π r3 + 1/3 Π r2 h = 1/3 Π r2 (2r + h)

= 1/3 x 22/7 x 21/10 x 21/10 (2 x 2.1 + 4) cm3 = 1/3 x 22/7 x 21/10 x 21/10 x 82/10 cm3

= 37.884 cm3

Therefore, Volume of water left = (770 - 37.884) cm3 = 732.166 cm3

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