The radius of the base of a cylinder is increasing at a rate of 7 millimeters per hour. the height of the cylinder is fixed at 1.51, point, 5 millimeters. at a certain instant, the radius is 12 millimeters.

what is the rate of change of the volume of the cylinder at that instant (in cubic millimeters per hour)?

The rate of change of the volume of the cylinder at that instant =

Step-by-step explanation:

Given:

Rate of increase of base of radius of base of cylinder = 7 mm/hr

Height of cylinder = 1.5 mm

Radius at a certain instant = 12 mm

To find rate of change of volume of cylinder at that instant.

Solution:

Let represent radius of base of cylinder at any instant.

Rate of increase of base of radius of base of cylinder can be given as:

Volume of cylinder is given by:

Finding derivative of the Volume with respect to time.

Plugging in the values given:

Using

(Answer)

Thus rate of change of the volume of the cylinder at that instant =

step-by-step explanation: