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Find volume of cone using 3.14pi

Find volume of cone using 3.14pi-example-1

1 Answer

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Answer:

d. 3391.2 ft³

Explanation:

You want the volume of a right circular cone with base diameter 18 ft and slant height 41 ft.

Height

The height of the cone can be found from the Pythagorean theorem:

h² +r² = 41² . . . . . . . where r is the radius, 9 ft

h = √(41² -9²) = √(1681 -81) = √1600 = 40

Volume

The volume is given by the formula ...

V = 1/3πr²h

V = 1/3(3.14)(9 ft)²(40 ft) = 3391.2 ft³

The volume of the cone is about 3391.2 cubic feet.

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Additional comment

The side lengths of the triangle we solved for the height are the integer values {9, 40, 41}. This is one of several Pythagorean triples that show up frequently in algebra, trig, and geometry problems. Others include {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}. Familiarity with these can save you some time when solving problems like this one.

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Find volume of cone using 3.14pi-example-1
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