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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?

1 Answer

5 votes

Answer:

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

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