Question

A solid consisting of a right circular cone of height 12 cm and radius 6 cm standing on a hemisphere of radius 6 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of the water displaced out of the cylinder, if the radius of the cylinder is 6 cm and height is 18 cm

Answer 1

Radius of a cone = Radius of a hemisphere = Radius of a cylinder

r = 6 cm

Height of a cone (h) = 12 cm

Volume of the water displaced = Volume of the solid inside = Volume of the cone + Volume of the hemisphere

= `1/3 pi"r"^2"h" + 2/3 pi"r"^3`

= `1/3pi"r"^2 ("h" + 2"r")"cm"^3`

= `1/3 xx 22/7 xx 6 xx 6 (12 + 12)"cm"^3`

= `1/3 xx 22/7 xx 6 xx 6 xx 24  "cm"^3`

Volume of water displaced = 905.14 cm³.