Question

A solid is in the front of a right circular cone mounted on a hemisphere . The diameter of the base of the cone , which exactly coincides with hemisphere , is 7cm and its height is 8cm . How much water , in cm3 , will be required to fill the vessel completely

Answer 1

given :-

diameter of both the hemisphere and cone = 7cm (since the cone completely coincides the hemisphere)

➡ it's radius = 7/2cm

height of the cone = 8cm

volume of the solid = volume of the cone + volume of the hemisphere

= 1/3πr²h + 2/3πr³

= (1/3 × 22/7 × 7/2 × 7/2 × 8) + (2/3 × 22/7 × 7/2 × 7/2 × 7/2)

= (1/3 × 11 × 7/2 × 4) + (1/3 × 22 × 7/2 × 7/2)

= 308/6 + 1078/12

= (616 + 1078)/12

= 1694/12

= 141.16cm³ (approximately)

hence, 141.16cm³ water will be required to fill the container completely