Multiple choice

A metallic right circular cone of height 36 cm and base radius 7 cm is melted and recast into a cuboid whose length and breadth are 22 cm and 6 cm, respectively. What is the height of the cuboid?

  1. 10 cm

  2. 12 cm

  3. 14 cm

  4. 16 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of the cone is (1/3) * pi * r^2 * h = (1/3) * (22/7) * 7 * 7 * 36 = 1848 cm^3. Equating this to the volume of the cuboid (l * b * h = 22 * 6 * h), we get 132 * h = 1848, so h = 14 cm.

AI explanation

By the conservation of volume, the volume of the cone equals the volume of the resulting cuboid. Using the cone volume formula, V = (1/3) * pi * 7^2 * 36, which gives V = (1/3) * (22/7) * 49 * 36 = 1848 cubic cm. Setting this equal to the cuboid volume of 22 * 6 * height gives 132 * height = 1848. Solving for height yields 14 cm. The result is 14 cm.

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