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

Answer:

The rate of change of volume of the cone with respect to radius is $\frac{2}{3}\pi\times rh$.

Step-by-step explanation:

radius of come = r

height of cone = h

Volume of cone

$V = \frac{1}{3}\pi\times r^2 h$

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.  

$\frac{dV}{dr}=\frac{1}{3}\pi\times {2r}h\\\\\frac{dV}{dr}=\frac{2}{3}\pi\times rh$