Question

The area of a circle is decreasing at a constant rate of 211 square meters per minute. At the instant when the area of the circle is 81 π 81π square meters, what is the rate of change of the radius? Round your answer to three decimal places.

Answer 1

Answer:

1.119 meter per minute

Step-by-step explanation:

Let intial (T1 = 0 seconds) area be A1 = 211 + 81π

So, Initial radius R1 = [(211 + 81π) / π ]^0.5 = 10.119311

When (T2=60 seconds i.e. 1 minutes) Area is 81π = A2

so, raduis R2 = 9

rate of change of radius = R2-R1 / T2-T1 = (10.119311 - 9)/1 = 1.1193  meter per minute

Answer 2

-3.731

Use the area to find the radius

81$\pi$ = $\pi$r^2

81 = r^2

9 = r

Plug in known values into the derivative, then use algebra to solve the equation.