Multiple choice

Base of a cone, hemisphere and cylinder are same and also heights of these figures are same then find the ratio of their volumes.

  1. 1 :2 :3

  2. 2 :3 : 2

  3. 3 :1: 2

  4. 3 :2 : 1

  5. None of these
Reveal answer Fill a bubble to check yourself
A 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 r = h, Volume cone = (1/3)pi*r^3, Volume hemisphere = (2/3)pi*r^3, Volume cylinder = pi*r^3. Ratio = (1/3) : (2/3) : 1 = 1 : 2 : 3.

AI explanation

Let r be the base radius and h be the height. The volume of the cone is one third pi r squared h. The volume of the hemisphere is two thirds pi r cubed, and since the height equals the radius, this becomes two thirds pi r squared h. The volume of the cylinder is pi r squared h, which equals three thirds pi r squared h. Comparing the numerators, the ratio of their volumes is 1 to 2 to 3.

Keep practicing — related questions