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Sand pours out of a right, conical container at a rate of 24 cubic feet per...

Sand pours out of a right, conical container at a rate of 24 cubic feet per minute. The initial height of the sand cone is 30 feet and the initial radius is 15 feet. When the height is 18 feet, the radius is 9 feet. How quickly is the height of the sand changing when the radius is of the sand cone is 2 feet?

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Answer #1

Properties of similar triangles

Ratio of corresponding sides of triangle is equal

--------------(1)

Volume of cone

Differentiating with respect to t

(dV/dt = 24 cubic feet per second

r=2 feet : h=2(2)=4 feet from equation (1))

feet per second

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