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Calculus/Volume and Surface Area question.

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Expert: - 3/31/2008


Question
The two radii of the frustum of a right circular cone are increasing at a rate of 4 centimeters per minute, and the height is increasing at a rate of 12 centimeters per minute. Find the rates at which the volume and surface area are changing when the two radii are 15 centimeters and 25 centimeters, and the height is 10 centimeters.  

Answer
For a cone that has a height larger radius R and a smaller radiud r.  The formula is pi(R^2 + Rr + r^2)h/3.  Make R and r functions of t. dR/dt and dr/dt are known as well as h.  Solve away!

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