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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