Multiple choice

The radius of the base of the height of a cone are $3\,cm$ and $5\,cm$ respectively whereas the radius of the base and height of a cylinder are $2\,cm$ and $4\,cm$ respectively. The ratio of the volume of cone to that of the cylinder is :

  1. $1:3$
  2. $15:8$
  3. $15:16$
  4. $45:16$
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C Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * 3^2 * 5 = 15 * pi. Volume of cylinder = pi * r^2 * h = pi * 2^2 * 4 = 16 * pi. Ratio = 15/16.

AI explanation

The volume of a cone is given by 1/3 * pi * r^2 * h, while the volume of a cylinder is pi * r^2 * h. For the cone, the volume is 1/3 * pi * 3^2 * 5 = 15pi cubic cm. For the cylinder, the volume is pi * 2^2 * 4 = 16pi cubic cm. The ratio of their volumes is 15pi to 16pi, which results in 15 : 16.

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