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?

Solution:

The circumference of circle is given as C = 2πr, where r = radius of the circle = 4m

Therefore dC/dt = 2πdr/dt

2πdr/dt = 0.5 m/min

dr/dt =[ 0.5/(2π)]

dr/dt = [0.25/π]m/min

Area of the circle(A) = πr²

dA/dt = d(πr²)

dA/dt = 2πrdr/dt

dr/dt = 0.5/(2π)

dA/dt = 2πr(dr/dt)

dA/dt = 2π(4)(0.5/2π)

dAdt = 2 m/minute

The rate of change of the area of the circle dA/dt = 2 m/minute

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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?

Summary:

The rate of change of the area of the circle when the radius is 4 meters is 2 m/minute