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The radius of a circle is increasing at the rate of 3 centimeters per second. At the instant the radius is 4cm, find a.) the rate of change of the area of the circle. B.) the rate of change of the circumference of the circle.

Question

The radius of a circle is increasing at the rate of 3 centimeters per second. At the instant the radius is 4cm, find a.) the rate of change of the area of the circle. B.) the rate of change of the circumference of the circle.

check_circleAnswer
Step 1

If r is the radius of he circle, then

Area of the Circle, A = πr2

Circumference of the circle, C = 2πr

dr/dt = 3 centimeters per second

At a particular instant of time, r = 4 cm

Step 2

Part (a)

Please see the white board. The rate of change of th...

dr
2Tr
dt
dA
A r2
dt
22
x 4 x 3 75.43
=2 x
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Image Transcriptionclose

dr 2Tr dt dA A r2 dt 22 x 4 x 3 75.43 =2 x

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Tagged in

Math

Calculus

Derivative

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