volume of a cone and a precious substance

A cone shaped container with a height of 15 feet and radius of 5 feet is filled with a substance that is worth $25/ft3. Find the total value of the substance in the container.


Solution

Find the volume of the substance in the container.

Volume = (πr2h)/3

Volume = (π×52×15)/3

Volume = (π×25×15)/3

Volume = (π×375)/3

Volume = π×(375/3)

Volume = π×(125)

Volume = (125π)ft3


Find the total value of the substance

If 1 ft3 is worth $25, then 125πft3 is worth $25 × 125π.

$25 × 125π = $3125π = $9812.5

The substance is worth $9812.5

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