Multiple choice

The height of a cone is $9 cm$ and the radius of the base is $7 cm$. The cone is melted and a cuboid is formed. The length of the base of the cuboid is $11 cm$ and breadth is $6 cm$. Find the height of the cuboid.

  1. $11cm$
  2. $9 cm$
  3. $7 cm$
  4. $5 cm$
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C Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * 49 * 9 = 147 * pi. Volume of cuboid = l * b * h_cuboid = 11 * 6 * h_cuboid = 66 * h_cuboid. Equating volumes: 66 * h_cuboid = 147 * pi. Using pi approx 22/7, 66 * h_cuboid = 147 * (22/7) = 21 * 22 = 462. h_cuboid = 462 / 66 = 7 cm.

AI explanation

Because the cone is melted to form the cuboid, their volumes must be equal. The volume of the cone is one third times pi times r squared times h, which yields one third times 22 divided by 7 times 7 squared times 9, equaling 462 cubic cm. The volume of the cuboid is length times breadth times height, so 462 equals 11 times 6 times the unknown height. Solving this gives a height of 7 cm.

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