Multiple choice

The radius of a right circular cone $A$ is $\dfrac {1}{5}$ of the radius of right circular cone $B$, and the height of right circular cone A is $\dfrac {1}{4}$ of the height of right circular cone B. Calculate the ratio of the volume of right circular cone A to the volume of right circular cone B.

  1. $\dfrac {1}{16}$
  2. $\dfrac {1}{25}$
  3. $\dfrac {1}{64}$
  4. $\dfrac {1}{80}$
  5. $\dfrac {1}{100}$
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E Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h. Ratio = (rA^2 * hA) / (rB^2 * hB). Given rA = rB/5 and hA = hB/4. Ratio = ((rB/5)^2 * (hB/4)) / (rB^2 * hB) = (1/25 * 1/4) = 1/100.

AI explanation

Using the volume of a cone formula V = (1/3) * pi * r^2 * h, let the radius of cone B be R and its height be H, making the radius of cone A equal to R/5 and its height H/4. The ratio of their volumes is [(1/3) * pi * (R/5)^2 * (H/4)] / [(1/3) * pi * R^2 * H], which simplifies to (1/25) * (1/4) = 1/100. The result is 1/100.

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