The Volume of a Right-Circular Cylinder of Radius R and Height

question 161

Essay

The volume of a right-circular cylinder of radius r and height h is .
Suppose the radius and height of the cylinder are changing with respect to time t. At a certain instant of time, the radius and height of the cylinder are 8 and 4 in. and are increasing at the rate of 0.5 and 0.1 in./sec, respectively.
How fast is the volume of the cylinder increasing?

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Definitions:

Great Depression

A severe worldwide economic downturn that took place during the 1930s, characterized by high unemployment, deflation, and a collapse in demand and investment.

Opportunity Cost

The cost of foregone alternatives when one option is chosen over another, representing the benefits that could have been gained by taking the alternate path.

Law of Increasing Cost

The principle that as production of a good expands, the opportunity cost of producing an additional unit rises.

Marginal Output

Marginal Output is the additional quantity of output that is produced by utilizing one more unit of a certain input, holding all other inputs constant, used to assess productivity improvements or decreases.