Multiple choice

If the volume of cylinder is $12436\ cm^{3}$ and radius and height of cylinder are in the ratio $2 : 3$, find its height.

  1. $21\ cm$
  2. $7\ cm$
  3. $14\ cm$
  4. $18\ cm$
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A Correct answer
AI explanation

Let the radius be 2x and the height be 3x based on the given ratio. The volume of a cylinder is pi times the radius squared times the height, so 12436 equals pi times (2x) squared times 3x. Using pi as 22/7, the equation becomes 12436 equals 22/7 times 12x cubed, which simplifies to x cubed equals 343. Taking the cube root gives x equals 7, so the height is 3 times 7, which is 21 cm.

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