Multiple choice

What would be the ratio of the volume of a right circular cone of base radius 28 cm and height 42 cm to the volume of another right circular cone of base radius 7 cm and height 14 cm?

  1. 48 : 1

  2. 42 : 1

  3. 34 : 7

  4. 24 : 1
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A Correct answer
Explanation

Volume of a cone = (1/3)*pi*r^2*h. Ratio = ((1/3)*pi*28^2*42) / ((1/3)*pi*7^2*14) = (28^2 * 42) / (7^2 * 14) = (4^2 * 3) / (1^2 * 1) = 16 * 3 = 48. The ratio is 48:1.

AI explanation

The formula for the volume of a right circular cone is (1/3) * pi * r^2 * h. The ratio of the two volumes is [(1/3) * pi * 28^2 * 42] / [(1/3) * pi * 7^2 * 14]. Canceling the common terms leaves (28 * 28 * 42) / (7 * 7 * 14), which simplifies to (4 * 4 * 3) / 1. This calculates to a ratio of 48 : 1. The result is 48 : 1.

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