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 $5$ cm, find the height of the cone.

  1. $10$ cm
  2. $15$ cm
  3. $18$ cm
  4. $24$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h_cone. Volume of cylinder = pi * r^2 * h_cyl. Since volumes are equal, (1/3) * h_cone = h_cyl. Given h_cyl = 5, h_cone = 3 * 5 = 15.

AI explanation

Since the material is converted, the volume of the cone equals the volume of the cylinder. Using the volume formulas, (1/3) * pi * r^2 * h_cone = pi * r^2 * h_cylinder. With the cylinder height given as 5 cm, the height of the cone calculates to 3 * 5 = 15 cm.

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