Question

As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. Find the rate at which the area of one side is changing when the diameter is 30 centimeters.

Answer 1

This is a neat one...okay, so you can automatically put down that the rate of change of the diameter is 0.01 cm/min. The change in the area is dependent on the change in the radius, and hence, the diameter:\[A = \pi*r^2 \rightarrow A = \pi*(d/2)^2 \rightarrow A = \pi*d^2/4\] and taking the derivative,\[dA/dt = \pi*2*d/4 = \pi*d*1/2.\] Plug in the diameter at a given time, and you should get the rate of change at that time.

Answer 2

Sorry, forgot to add -- multiply by the rate of change of the diameter, if I'm not mistaken.