A spherical balloon is punped at the rate of `10 "inch"^(3) min^(-1)`, the rate of increase of its radius if its radius is 15 inch is

Options

A. `1/(30 pi) "inch" min^(-1)`
B. `1/(60 pi)"inch" min^(-1)`
C. `1/(90pi) "inch" min^(-1)`
D. `1/(120pi) "inch" min^(-1)`

Answer

C

Explanation

Let `V` be the volume and `r` be the radius of the balloon at any time `t`
`:.V=4/3pir^(3)`
`implies(dV)/(dt)=4/3 pi(3r^(2))(dr)/(dt)`
`implies10=(4pi)/3 . 3. (15)^(3)(dr)/(dt)`
`implies (dr)/(dt)=1/(90pi)` inch/min