Mensuration-53

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An ice-cream cone is the union of a right-circular cone and a hemisphere that has the same (circular) base as the cone.
Find the volume of the ice cream if the height of the cone is 9 cm and the radius of its base is 2.5 cm.

Solution: Radius of the base = 5/2 cm. Height of the cone = 9 cm.

Volume of the cone = 1/3 Π r2 h = 1/3 x 22/7 x 5/2 x 5/2 x 9 = 825/14 cu.cm

Volume of the hemisphere = 1/2 (4/3 Π r3)

= 1/2 x 4/3 x 22/7 x 5/2 x 5/2 x 5/2 = 1375/42 cu. cm

Volume of ice-cream cone = (825/14 + 1375/42) cm3 = (2475 + 1375) / 42 = 3850/42 = 275/3 = 91-2/3 cm3

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