Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6.

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Question

​Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6.
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A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

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

A = πr^2

We can differentiate both sides with respect to time:

dA/dt = 2πr(dr/dt)

We know that dr/dt = -4 (negative sign because the radius is decreasing).

And we're given that r = 6.

So plugging these values in:

dA/dt = 2π(6)(-4) = -48π

This means that the area is decreasing at a rate of 48π square centimeters per minute when the radius is 6.

Simplifying this,

dA/dt ≈ -150.8

So the rate of change of area is approximately -150.8 square centimeters per minute.

Therefore, the answer is D) 11ea8970_69a5_d6e5_861b_73702b18561e_TB1301_11.

​AreaThe Radius,r,of a Circle Is Decreasing at a Rate of 4

AreaThe Radius,r,of a Circle Is Decreasing at a Rate of 4