Question

In: Math

The volume of a right circular cylinder with base radius ? and height ℎ is given...

The volume of a right circular cylinder with base radius ? and height ℎ is given by: ? = ??^2ℎ. If the base radius is decreasing at a rate of 3 inches per minute and the height is increasing at a rate of 2 inches per minute, at what rate is the volume of the cylinder changing when the radius is 8 inches and the height is 3 inches. Will the volume be increasing or decreasing at this instant? Be sure to answer both questions and be sure to include units in your answer.

Solutions

Expert Solution

If the derivative of function is increasing, the value will have a positive sign.
If the derivative of function is decreasing, the value will have a negative sign.

Given the rate of the base radius is decreasing ( when the rate is given, the derivative is taken with respect to time), so the derivative is negative.

Given the rate of base radius is increasing ( when the rate is given, the derivative is taken with respect to time) , so the derivative is positive.

Rate at which volume changes is given by:

EQUATIONS USED

But we already have the values

Rate is the volume of the cylinder changing when the radius is 8 inches and the height is 3 inches

that means when r = 8 and h = 3 , dV/dt =

Since the derivative has a negative value , the function (here volume) is decreasing.

milcah answered 1 year ago

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