5 persons will live in a tent. If each person requires `16 m^(2)` of floor area and `100 m^(3)` space for air then the height of the cone of the smallest size to accommodate these persons would be

Options

A. 16 m / 16 मी
B. 20 m / 20 मी
C. `10.25` m / 10.25 मी
D. `18.75` m / 18.75 मी

Answer

D

Explanation

वृत्ताकार फर्श का क्षेत्रफल `= 5 xx 16 = 80 m ^(2)`
`implies pi r ^(2) = 80 m ^(2)`
तंबु का आयतन `= 5 xx 100`
`implies (1)/(3) pi r ^(2) h = 500 m ^(3)`
`implies (80)/(3) h = 500`
`implies h = ( 500 xx 3)/( 80) = 18 . 75 m`