Multiple choice

A right circular cone is of height $3.6$ cm and radius of its base is $1.6$ cm . It is melted and recasted into a right circular cone with radius of its base $1.2$ cm. Find the height of the cone so formed.

  1. $6.4$ cm
  2. $6$ cm
  3. $4$ cm
  4. $4.8$ cm
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A Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h. Since volume is constant, r1^2 * h1 = r2^2 * h2. (1.6)^2 * 3.6 = (1.2)^2 * h2. 2.56 * 3.6 = 1.44 * h2. h2 = (2.56 * 3.6) / 1.44 = 6.4 cm.

AI explanation

Because the volume remains constant when the cone is melted and recast, use the cone volume formula, 1 over 3 times pi times radius squared times height. The original volume is 1 over 3 times pi times 1.6 squared times 3.6, and the new volume is 1 over 3 times pi times 1.2 squared times the new height. Equating the volumes and canceling pi and 1 over 3 gives 1.6 squared times 3.6 equals 1.2 squared times the new height. Solving this, the new height equals 2.56 times 3.6 divided by 1.44, which is 6.4 centimeters.

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