A conical tent is required to accommodate 157 persons each person must have 2 m`m^(2)` of space on the ground and 15 `m^(3)` of air to breath .Find the height of the tent , also calculate the slant height.

Explanation

1 person needs `2m^(2)` of space.
`therefore` 157 persons needs `2xx157 m^(2)` space on the ground.
`therefore pi r^(2)=2xx157`
`therefore r^(2)=(2xx157)/(3.14)=100 rArr r=10 m`

Also 1 person needs `15m^(3)` of air
`therefore` 157 persons need `15xx157 m^(3)` of air.
`therefore (1)/(3)pi r^(2)h=15xx157`
`rArr h=(15xx157xx3)/(3.14xx100)=22.5 m`
`therefore l^(2)=h^(2)+r^(2)`
`= (22.5)^(2)+(10)^(2)`
`=606.25`
`therefore l= sqrt(606.25)=24.62 m`