Multiple choice

Quantity A Height of a right circular cone with volume 12π cubic inches and radius 2 inches Quantity B Height of a right circular cone with volume 18π cubic inches and radius 3 inches

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
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A Correct answer
Explanation

Volume = (1/3) * pi * r^2 * h. For A: 12pi = (1/3) * pi * 2^2 * hA => 12 = (4/3) * hA => hA = 9. For B: 18pi = (1/3) * pi * 3^2 * hB => 18 = 3 * hB => hB = 6. Quantity A (9) > Quantity B (6).

AI explanation

Using the cone volume formula, V equals one third times pi times r squared times h, the height for Quantity A is 12 times pi divided by one third times pi times 2 squared, which equals 9 inches. The height for Quantity B is 18 times pi divided by one third times pi times 3 squared, which equals 6 inches. Since 9 inches is greater than 6 inches, Quantity A is greater.

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