Multiple choice

A solid cylinder of base radius 12 cm and height 15 cm is melted and recasted into n toys, each in the shape of a right circular cone of height 9 cm mounted on a hemisphere of radius 3 cm. The value of n is

  1. 27

  2. 64

  3. 48

  4. 54
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = pi * 12^2 * 15 = 2160 * pi. Volume of one toy = volume of cone + volume of hemisphere = (1/3 * pi * 3^2 * 9) + (2/3 * pi * 3^3) = 27 * pi + 18 * pi = 45 * pi. n = 2160 * pi / 45 * pi = 48.

AI explanation

Using the volume conservation formula, the volume of the solid cylinder equals the combined volume of the n toys, giving pi*12^2*15 = n*(2/3*pi*3^3 + 1/3*pi*3^2*9). Solving the cone and hemisphere volumes gives the volume of one toy as 18pi + 27pi = 45pi cubic cm, and the cylinder volume as 2160pi cubic cm. Equating the volumes results in 2160pi = n*45pi, so n = 48.

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