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CONE VOLUME

A pile of gravel is shaped like a cone and has a radius of 6 ft and a height of 9 ft. Garden Landscaping Company purchases some of this gravel. After the gravel that Garden Landscaping Company purchases is removed, the pile has a radius of 3 ft and a height of 6 ft.

How much gravel did Garden Landscaping Company purchase?
Use 3.14 to approximate pi and express your final answer in tenths.



Answer :

iGreen
Find the volumes of the two cones and subtract.

V = 1/3 * pi * r^2 * h

V = 1/3 * 3.14 * 6^2 * 9

Simplify exponent:

V = 1/3 * 3.14 * 36 * 9

Multiply:

V = 339.12

V = 1/3 * pi * r^2 * h

V = 1/3 * 3.14 * 3^2 * 6

Simplify exponent:

V = 1/3 * 3.14 * 9 * 6

Multiply:

V = 56.52

Subtract the two volumes:

339.12 - 56.52 = 282.6

So the Garden Landscaping Company purchased 282.6 ft^3 of gravel.

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