Multiple choice

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 9 cm, the height of the cone is-

  1. 3 cm

  2. 9 cm

  3. 15 cm

  4. 27 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of cone = (1/3)πr²h. Volume of cylinder = πr²H. Setting equal with same radius: (1/3)πr²h = πr²H. Cancelling πr²: h/3 = H, so h = 3H. Given H = 9 cm, we get h = 27 cm. The cone's height must be 3 times the cylinder's height when radii are equal and volumes are equal.

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