Multiple choice

Choose the correct answers from the alternatives given. If a cone, a hemisphere and a cylinder stand on the same base and have height equal to the radius of the base, find out the ratio of their volumes.

  1. 1:3:2

  2. 2:3:1

  3. 3:2:1

  4. 1:2:3
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D Correct answer
Explanation

Let radius = r, height = r. Volume of cone = (1/3)pi*r^2*h = (1/3)pi*r^3. Volume of hemisphere = (2/3)pi*r^3. Volume of cylinder = pi*r^2*h = pi*r^3. Ratio = (1/3) : (2/3) : 1 = 1 : 2 : 3.

AI explanation

Let the common base radius be r, meaning the common height is also r. The volumes are (1/3)πr^3 for the cone, (2/3)πr^3 for the hemisphere, and πr^3 for the cylinder. Dividing by (1/3)πr^3 gives the ratio 1 : 2 : 3. The result is 1:2:3.

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