Multiple choice

Two solid cylinders, one with diameter $60$ cm and height $30$ cm and the other with radius $30$ cm and height $60$ cm are melted and recasted into a third solid cylinder of height $10$ cm. Find the diameter of the cylinder formed.

  1. $150$ cm
  2. $180$ cm
  3. $140$ cm
  4. $160$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of the first cylinder is pi * 30^2 * 30 = 27000 * pi. The volume of the second is pi * 30^2 * 60 = 54000 * pi. The total volume is 81000 * pi, which must equal pi * r^2 * 10, so r^2 = 8100, r = 90. The diameter is 2 * r = 180 cm.

AI explanation

By the principle of conservation of volume, the volume of the new cylinder equals the sum of the volumes of the two original cylinders, calculated as pi times 30 squared times 30 plus pi times 30 squared times 60. The total volume is 81000 times pi, and equating this to the new cylinder's volume formula, pi times the new radius squared times 10, gives the new radius squared equals 8100. Taking the square root gives a new radius of 90 centimeters, making the diameter twice that, which is 180 centimeters.

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