Multiple choice

A right circular cone has a volume of 162π cubic inches and a height of 6 inches. What is the radius, in inches, of the base of the cone?

  1. 5

  2. 6

  3. 7

  4. 9
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D Correct answer
Explanation

Volume of a cone V = (1/3) * pi * r^2 * h. 162 * pi = (1/3) * pi * r^2 * 6. 162 = 2 * r^2. r^2 = 81, so r = 9.

AI explanation

Using the volume formula for a right circular cone, V = 1/3πr^2h, we substitute the known values to get 1/3 * π * r^2 * 6 = 162π. Simplifying the left side gives 2πr^2 = 162π, and dividing both sides by 2π results in r^2 = 81. Taking the positive square root gives a radius of 9 inches.

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