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A right circular cone has a volume of 162m cubic inches. If the height is 6 inches, determine the length of

the radius and diameter of the base of the cone.

1 Answer

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Explanation:

We can use the formula for the volume of a right circular cone, which is V = (1/3)πr^2h, where V is the volume, r is the radius of the base, h is the height, and π is the constant pi.

We are given that the volume of the cone is 162 cubic inches and the height is 6 inches, so we can substitute these values into the formula and solve for the radius:

162 = (1/3)πr^2(6)

Simplifying:

54 = πr^2

Dividing both sides by π:

r^2 = 54/π

Taking the square root of both sides:

r = sqrt(54/π) ≈ 4.115

Therefore, the radius of the base of the cone is approximately 4.115 inches.

To find the diameter of the base, we can multiply the radius by 2:

d = 2r ≈ 8.23

Therefore, the diameter of the base of the cone is approximately 8.23 inches.

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