Multiple choice

A solid metal cone with radius of base $12$ cm and height $24$ cm, is melted to form spherical solid balls of diameter $6$ cm each. Find the number of balls thus formed.

  1. $30$
  2. $31$
  3. $32$
  4. $34$
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C Correct answer
Explanation

Volume of cone = (1/3)*pi*r^2*h = (1/3)*pi*144*24 = 1152*pi. Volume of sphere = (4/3)*pi*r^3 = (4/3)*pi*3^3 = 36*pi. Number of balls = 1152*pi / 36*pi = 32.

AI explanation

Using the cone volume formula (1/3)pi*r^2*h, the initial volume is (1/3)*pi(12^2)24 = 1152*pi cubic cm. The radius of each spherical ball is half the diameter, which is 3 cm. Applying the sphere volume formula (4/3)*pi*r^3 gives the volume of one ball as (4/3)*pi(3^3) = 36*pi cubic cm. Dividing the total cone volume by the volume of one ball, 1152*pi / 36*pi, gives exactly 32. The result is 32.

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