The radius of a cylinder is increasing at the rate of `3ms^(-1)` and its altitude is decreasing at the rate of `4ms^(-1)`. The rate of change of volume when radius is `4m` and altitude is 6m is

Options

A. `80 pi cums^(-1)`
B. `144pi cu ms^(-1)`
C. `80 cu ms^(-1)`
D. `64 cu ms^(-1)`

Answer

A

Explanation

Let `h` and `r` be the height and radius oif cylinder.
Givne `(dr)/(dt)=3m//s, (dh)/(dt)=-4m//s`
Let volume of cylinder `V=pir^(2)h`
`implies (dV)/(dt)=pi[r^(2)(dh)/(dt)+h.2r(dr)/(dt)]`
At `r=4m` and `h=6m`
`(dV)/(dt)=pi[-64+144]=80pi` cu m/s