Multiple choice

Ramesh bought a decorative item made of some kind of wood consist of a cylindrical body, hemisphere and a cone. What is the ratio of the volume of cone, hemisphere and cylinder if they all have same height and radius?

  1. 2 : 1 : 3

  2. 1 : 3 : 2

  3. 2 : 3 : 1

  4. 1 : 2 : 3
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D Correct answer
Explanation

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

AI explanation

Using the volume formulas for a cone, a hemisphere, and a cylinder, we compare their volumes with radius r. The volumes are 1/3*pi*r^3, 2/3*pi*r^3, and pi*r^3 respectively. Multiplying the cylinder volume by 3/3 to get a common denominator shows the ratio is 1/3 : 2/3 : 1. The result is 1 : 2 : 3.

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