The radius of a circle is increasing at a rate of 7 centimeters per minute. Find the rate of change of the area when the radius is 3 centimeters. Round your answer to one decimal place. The rate of change of the area is Number Units

Sol59:

We know that the area of a circle is given by the formula: A = pr^2

Taking the derivative of both sides with respect to time (t), we get:

dA/dt = 2pr(dr/dt)

We are given that dr/dt = 7 cm/min and r = 3 cm.

Substituting these values, we get:

dA/dt = 2p(3)(7) = 42p

Rounding this to one decimal place, we get:

dA/dt 131.95 cm^2/min

Therefore, the rate of change of the area when the radius is 3 centimeters and increasing at a rate of 7 centimeters per minute is approximately 131.95 cm^2/min.