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Expert: - 12/30/2008


Question
Hey, The radius of a spherical ball is decreasing at a constant rate of 3 cm per second.  I don't know how to find , in cubic centimeters per second, the rate of change of the volume of the ball when the radius is 5 cm.

Answer
We know that the volume of a sphere is 4πr^3/3.

Here, r is 5 cm. so the volume is 500π/3.

To find the rate in change in volume, take the derivative.

Since V = 4πr^3/3, dV = 4πrē dr.

It is know that the radius is 5cm and the rate of change -3 (since it is decreasing.  Since r is know, dr is known, and π=3.1416, dV can be found by putting them in the equation for dV.  

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