(1 point) A rock is thrown into a still pond and causes a circular ripple. If the radius of the ripple is increasing at a rate of 4 feet per second, how fast is the circumference changing when the radius is 20 feet?

1 Answer
Sean
Mar 31, 2018

#25.13# feet per second

Explanation:

.

The formula for the circumference of a circle is:

#C=2pir# where are is the radius.

Let's take the derivatives of both sides with respect to time #t#:

#(dC)/dt=2pi(dr)/dt#

#(dr)/dt=4# feet per second

#(dC)/dt=2pi(4)=8pi=25.13# feet per second

It does not matter what the radius is at any moment. The rate of change of the circumference depends only on the rate of change of the radius which is constant.

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