Sand Is Falling into a Conical Pile So That the Radius

question 160

Essay

Sand is falling into a conical pile so that the radius of the base of the pile is always equal to one half its altitude. If the sand is falling at the rate of 5 cubic feet per minute, how fast is the altitude of the pile increasing when the pile is 3 feet deep?

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Definitions:

Reselling

The act of selling a product or service again, possibly after acquiring, refurbishing, or repackaging it.

Perfect Price Discrimination

A situation where a seller charges the maximum possible price for each unit consumed that each consumer is willing to pay, thus capturing the entire consumer surplus.

Consumer Surplus

The difference between the total amount that consumers are willing and able to pay for a good or service and the total amount that they actually do pay.

Market Price

The current price at which an asset or service can be bought or sold.