The radius of a cylinder is increasing at the rate 2cm/sec. and its altitude is decreasing at the rate of 3cm/sec. Find the rate of change of volume when radius is 3 cm and altitude 5 cm.

Options

A. `11pi cm^(3)s^(-1)`
B. `44pi cm^(3) s^(-1)`
C. `23 pi cm^(3) s^(-1)`
D. `33 pi cm^(3) s^(-1)`

Answer

D

Explanation

Now volume of cylinder `V=pi r^(2)h`
Given `(dr)/(dt)=2,(dh)/(dt)=-3,r=3` and `h=5`
`:.(dV)/(dt)=pi[r^(2) . (dh)/(dt) +h(2r)(dr)/(dt)]`
`=pi[(9(-3)+30(2)]=pi [60-27]`
`=33pi cm^(3)s^(-1)`