SOLUTION: Find the rate at which the volume of a right circular cylinder of constant altitude 10ft changes with respect to its diameter when the radius is 5ft is zero.

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Question 1119545: Find the rate at which the volume of a right circular cylinder of constant altitude 10ft changes with respect to its diameter when the radius is 5ft is zero.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The statement of the problem makes no sense: "...when the radius is 5 ft is zero."

I can only assume that the question was supposed to read "... when the radius is 5 feet."

The formula for the volume of a cylinder is

%28pi%29%28r%5E2%29%28h%29

The height h is fixed at 10. The problem asks for the rate of change of volume with respect to diameter; so we need the volume equation in terms of the diameter:

%28pi%29%28%28d%2F2%29%5E2%29%2810%29+=+%285pi%2F4%29%28d%5E2%29

Then dV/dd is

%285pi%2F2%29%28d%29

When the radius is 5, the diameter is 10, so when the radius is 5 the rate of change of volume with respect to diameter is

%285pi%2F2%29%2810%29+=+25pi