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

Explanation

Let the radius of the base of the conical tent be r metres and its height be h metres.
Area of the base `= (4 xx 11) m^(2) = 44 m^(2) rArr pi r^(2) = 44m^(2)`..(i)
Volume of the cone `= (20 xx 11) m^(3) = 220 m^(3)`
`rArr (1)/(3) pi r^(2) h = 220 m^(3) rArr pi r^(2) h = 660 m^(3)`...(ii)
On dividing (ii) by (i), we get
`(pi r^(2)h)/(pi r^(2)) = (660 m^(3))/(44m^(2)) rArr h = 15 m`
Hence, the height of the tent is 15 metres