How fast is the area of a circle increasing when the circumference equals 8 feet and the circumference is..?

How fast is the area of a circle increasing when the circumference equals 8 feet and the circumference is increasing at a rate of 7 feet per minute? The area is increasing at ? square feet per minute.

Thanks in advance for the help!

C = 2pi*r

A = pi*(C / 2pi)^2
A = C^2 / 4pi
dA / dt = (1 / 4pi) *2C * dC / dt
dA / dt = (1 / 4pi) *2(8) * (7)
dA / dt = 112 / (4pi)
dA / dt = 28 / pi

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One Response to “How fast is the area of a circle increasing when the circumference equals 8 feet and the circumference is..?”

michaelempeigne on January 31st, 2010 at 9:45 am

C = 2pi*r

A = pi*(C / 2pi)^2
A = C^2 / 4pi
dA / dt = (1 / 4pi) *2C * dC / dt
dA / dt = (1 / 4pi) *2(8) * (7)
dA / dt = 112 / (4pi)
dA / dt = 28 / pi
References :

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