Question

The radius of a circle is increasing at a constant rate of 0.5 meter per second. What is the rate of increase in the circumference of the circle at the instant when the radius of the circle is 3 meters?

A. 0.5 m/sec
B. 1.5 m/sec
C. Pi m/sec
D. 3pi m/sec

Answer 1

π

Explanation:

It is given that the radius is increasing at a rate of 0.5 m/s. That means

dr/dt=0.5 this is positive because it is increasing

The question is asking to find the circumference rate at r=3, that means, our goal is to find dC/dt, C for circumference

Now we need a formula relates r and C, which is C=2πr

Now we have to take the derivative of both sides

dC/dt=2π(dr/dt) let's plugin the value of dr/dt

dC/dt=2π(0.5) = π