Question

A circular plate is being heated. Its radius is increasing at the rate of 0.02 in/min. At what rate is the area of the plate increasing at the instant when the radius is 6 inches.

Answer 1

Answer:

$\frac{dA}{dr} =2\pi (6in) (0.02 \frac{in}{min})=0.754 \frac{in^2}{min}$

Step-by-step explanation:

Data given

$\frac{dr}{dt}= 0.02 \frac{in}{min}$

r = 6 in

Solution to the problem

We know that the area for a circle is given by:

$A= \pi r^2$

We want to find at what rate is the area of the plate increasing at the instant when the radius is 6 inches. So we need to take partial derivates in both sides of the equation for the area, and if we do this we got:

$\frac{dA}{dr} = 2\pi r \frac{dr}{dt}$

Since we have all the values provided we just need to replace and we got:

$\frac{dA}{dr} =2\pi (6in) (0.02 \frac{in}{min})=0.754 \frac{in^2}{min}$