Multiple choice

The radius of right cylinder A is twice the radius of right cylinder B, and the height of cylinder B is twice the height of cylinder A. What is the ratio of the volume of cylinder A to the volume of cylinder B?

  1. $2$
  2. $4$
  3. $1$
  4. $3$
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A Correct answer
Explanation

Volume of cylinder = pi * r^2 * h. Cylinder A: rA = 2rB, hA = hB/2. Volume A = pi * (2rB)^2 * (hB/2) = pi * 4rB^2 * hB/2 = 2 * pi * rB^2 * hB. Volume B = pi * rB^2 * hB. Ratio A/B = 2.

AI explanation

Using the volume of a cylinder formula, V = pi * r^2 * h, let the radius of cylinder B be r and its height be 2h, making cylinder A's radius 2r and height h. The volume of cylinder A is pi * (2r)^2 * h = 4 * pi * r^2 * h, while the volume of cylinder B is pi * r^2 * (2h) = 2 * pi * r^2 * h. The ratio of their volumes is 4/2, which equals 2.

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