related rates (one forumla)

Question

The height of a cylinder is increasing at a constant rate of 7 inches per minute. The volume remains a constant 889 cubic inches. At the instant when the radius of the cylinder is 9 inches, what is the rate of change of the radius? The volume of a cylinder can be found with the equation V=πr2h. Round your answer to three decimal places.

Answer 1

Answer:

The rate of change of the height is approximately - 5.4344 in /min

Step-by-step explanation:

From Geometry we know that volume of cylinder (), measured in cubic inches, is expressed by:

 (1)

Where:

 - Radius, measured in inches.

 - Height, measured in inches.

Given that volume remains constant, the expression for the rate of change of the height (), measured in inches per minute, is:

 (2)

Where  is the rate of change of the radius, measured in inches per minute.

If we know that r = 9, r°= 7 and V = 889, then the rate of change of the height is:

h° = -2*7*889/(π*9³)

h° = - 5.4344

The rate of change of the height is approximately - 5.4344 in /min .

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