This of course is the area of the square minus the area of the circle.

Taking the derivative with respect to time, we have

.

Calling on our resident algebraist, we obtain

When the circle area is 36pi, we need to solve

Doing so, we have r=6 at this point in time.

Plugging in r and (dr/dt) to the dA/dt equation, we have

Now click cir.squ and check your answer with the sketch. Click "show", and find the right formula(s). You will need to have dC/dt set to 1.58. Then set the radius to 6. Explain the formulas in the sketch you are using.

What would happen to dA/dt above if the radius of the circle doubled? Tripled?

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