Question

The volume of a right circular cylinder with radius r and height h is Vrh. Is the volume an increasing or decreasing function of the radius at a fixed height%E2%80%8B (assume r0 and h%E2%80%8B0)?

Answer 1

The rate of change of volume of the cone with respect to radius is
`(2)/(3)\pi* rh\\`.

Explanation:

radius of come = r

height of cone = h

Volume of cone

`V = (1)/(3)\pi* r^2 h`

As the height is constant, the rate of change of volume with respect to radius is given by the derivative of volume with respect to radius.

`(dV)/(dr)=(1)/(3)\pi* {2r}h\\\\(dV)/(dr)=(2)/(3)\pi* rh\\\\`