Question

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. Use [π = `22/7`]

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.

Answer 1

Radius (r) of hemispherical part = Radius (r) of conical part = 60 cm

Height (h₂) of conical part of solid = 120 cm

Height (h₁) of cylinder = 180 cm

Radius (r) of cylinder = 60 cm

Volume of water left = Volume of cylinder − Volume of solid

= Volume of cylinder − (volume of cone + volume of hemisphere)

`= pi"r"^2"h"_2 - (1/3pi"r"^2"h"_2 + 2/3pi"r"^3)`

`= pi(60)^2(180) − (1/3pi(60)^2 xx 120 + 2/3pi(60)^3)`

`= π(60)^2 [(180) − (40+40)]`

= π(3600) × (100)

= 360000π cm³

= 1131428.57142 cm³

= `1131428.57142/100000 m^3   ...[∵ 1  cm = 1/100  m]`

= 1.13142857142

= 1.131 m³ (approx)