Question

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.

Answer 1

1 person needs 2 `m^(2)` of space
157 persons needs `2xx157 m^(2)` space on the ground.
`pi^(2)=2xx157`
`r^(2)=(2xx157)/(3.14)=100 rarr r=10 m`
Also 1 person needs 15`m^(3)` of air.
157 persons need `15xx157 m^(3)`of air.
`(1)/(3) pir^(2)h =15xx157`
`h=(15xx157xx3)/(3.14xx100)=22.5 m`
`(l^(2))=(h^(2)+r^(2)=(22.5)^(2)+10^(2))=606.25`
`l=sqrt(606.25)=24.62 m`