Question

The volume V of a right circular cylinder of radius r and height h is V=πr2h. (a) How is dVdt related to drdt if h is constant and r varies with time? (Enter drdt as dr/dt.)

Answer 1

Explanation:

Given that the volume V of a right circular cylinder of radius r and height h is
`V=\pi r^2h`

To find rate of change of V with respect to rate of change of radius

Here given that h is constant

So differentiation with respect to t gives

`(dv)/(dt) =2\pi r h (dr)/(dt)`

This would be dv/dt i.e. rate of change of volume with respect to time in terms of dr/dt

This varies whenever r varies