Question

1. If the radius of the circle increases at the rate of 0.01 cm per second, find the rate of change of the area when the radius is 3 cm long

Answer 1

Solution.

We know that the area of the circle determine as $S=πr^2.$ Also we have $\frac{dr}{dt}=0.01$ cm/sec, because the radius of the circle increases at the rate of 0.01 cm per second.

Find $\frac{dS}{dt}=2πr\frac{dr}{dt}.$ Such as r=3 cm, then $\frac{dS}{dt}=2π•3•0.01=0.06π$ cm²/sec or 0.1884 cm²/sec.

Answer. 0.1884 cm²/sec