Find the average rate of change of the area of a circle with respect to its radius r as r changes from 5 to 6 .
A) $11 \pi$
B) $36 \pi$
C) $8 \pi$
D) $6 \pi$
E) $12 \pi$

Question

Quizplus · Accepted Answer

The area of a circle is given by $ A = \pi r^2 $. The average rate of change of the area with respect to the radius as $ r $ changes from 5 to 6 is $\frac{\pi(6^2) - \pi(5^2)}{6 - 5} = \frac{36\pi - 25\pi}{1} = 11\pi$.

Find the Average Rate of Change of the Area of a Circle