Question

A conical tent is accommodate to 11 persons each person must have 4 sq. metre of the space on the ground and 20 cubic metre of air to breath. Find the height of the cone.

Answer 1

Area of the base = 11 x 4 = 44 m²

and Volume of the cone = 11 x 20 = 220 m³

`1/3` x πR²h = 220 m³

Area of the base = πR²

∴ πR² = 44

∴ R² = `44/22 xx 7`

∴ R² = 14

∴ R = `sqrt14`

By equations (i) and (ii), we get

`1/3 xx 22/7 xx sqrt14 xx sqrt14 xx h = 220`

h = `(220 xx 3)/(22 xx 2)`

h = `30/2`

= 15 m.