Right triangle ABC, shown, has a vertical leg 6 inches long and a hypotenuse 10 inches long. If the triangle was rotated 360 degrees around the vertical leg to form a right circular cone, what would be the volume of this cone, in cubic inches?
A. 32
B. 96
C. 128
D. 288
E. 384

Right triangle ABC shown has a vertical leg 6 inches long and a hypotenuse 10 inches long If the triangle was rotated 360 degrees around the vertical leg to for class=

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Answer:

The answer to your question is the letter D. 288 in³

Step-by-step explanation:

Data

Radius = 6 in

height = ?

g = 10 in

Volume = ?

Formula

Volume of a cone = πr²h / 3

Process

1.- Find height using the Pythagorean theorem

            height² = 10² - 6²

                         = 100 - 36

                         = 64

            height = 8

2.- Find the volume of the cone

            Volume = π(6)²(8)

Simplification

            Volume = π(36)(8)

Result

             Volume = 288π in³

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