Answer:
45π cm³/s
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