Question

The circumference of the circle is increasing at a rate of 0.5 meters per minute. What's the rate of change of the area of the circle when the radius is 4 meters?

Answer 1

2 meter square per minute

Explanation:

Given the circumference is of the circle is increasing at a rate of 0.5 m/minute

We know that C = 2πr

We know that the area of the circle(A) = π
`r^2`

Let π=a

`r=(C)/(2a)`

A = a
`((C)/(2a))^2`

`A=(C^2)/(4a)`

Differentiate both sides with respect to time

`(dA)/(dt)=(C)/(2a)(dC)/(dt)`

C at r= 4 is C = 8a

Given
`(dC)/(dt)` = 0.5

`(dA)/(dt)=(8a)/(4a)` = 2