A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

Here, the volume of water left will be = Volume of cylinder – Volume of solid

Given,

Radius of cone (r) = 60 cm,

Height of cone (h) = 120 cm

Radius of cylinder (r) = 60 cm

Height of cylinder (H) = 180 cm

Radius of hemisphere (r) = 60 cm

Volume of the water left in the cylinder = volume of the cylinder - volume of the hemisphere - volume of the cone

= πr²H - 2/3 πr³ - 1/3 πr²h

= (1/3)πr² (3H - h - 2r)

= 1/3 × 22/7 × 60 cm × 60 cm × (3 × 180 cm - 120 cm - 2 × 60 cm)

= 1/3 × 22/7 × 60 cm × 60 cm × 300 cm

= 7920000/7 cm³

= 1131428.57/1000000 m³

= 1.13142657 m³

Thus, the volume of water left in the cylinder is 1.131 m³.