A cylinder is being filled such that the height of its contents is increasing at a rate of 5 cm /s. What is the rate of change of the volume if r = 3 and V = πr2h?

45π cm³/s

Step-by-step explanation:

Given the formula for calculating volume of a cylinder to be;

V = πr²h

Rate of change of volume = dV/dt since rate means time.

If the height of its contents is increasing at a rate of 5 cm /s, this can be expressed as;

dh/dt where h is the height of its content

dh/dt =5cm/s

According to chain rule;

dV/dt = dV/dh × dh/dt

Where dV/dh can be gotten by differentiating the volume (V) of the cylinder with respect to the height (h)

dV/dh = πr²

dV/dh at r = 3 will give;

dV/dh = π(3)² = 9π cm²

dV/dt = 9πcm² × 5cm/s

dV/dt = 45π cm³/s

The rate of change of volume is 45π cm³/s