Multiple choice

A cone and a hemisphere have equal radii, and the height of the cone is equal to the radius. What is the ratio of their volumes?

  1. 1:2

  2. 2:1

  3. 1:1

  4. 1:3
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A Correct answer
Explanation

Volume of cone = 1/3 * pi * r^2 * h. Since h = r, V_cone = 1/3 * pi * r^3. Volume of hemisphere = 2/3 * pi * r^3. Ratio = (1/3) / (2/3) = 1:2.

AI explanation

The volume of a cone is calculated as (1/3) * pi * r^2 * h, so with a height equal to its radius r, its volume is (1/3) * pi * r^3. The volume of a hemisphere is (2/3) * pi * r^3. Finding the ratio of the cone's volume to the hemisphere's volume gives [(1/3) * pi * r^3] / [(2/3) * pi * r^3], which simplifies to 1:2.

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