Multiple choice

A cylinder of height 15 cm and radius 7 cm is melted and recast into two equal cylinders, each of height 7.5 cm. The radius of each cylinder is

  1. 7 cm

  2. 7.5 cm

  3. 6.5 cm

  4. 6 cm
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A Correct answer
Explanation

Volume of original cylinder = pi * 7^2 * 15 = 735 * pi. Two new cylinders have volume = 2 * (pi * r^2 * 7.5) = 15 * pi * r^2. 735 * pi = 15 * pi * r^2. r^2 = 735 / 15 = 49. r = 7.

AI explanation

Since the original cylinder is melted and recast into two equal cylinders, the volume is preserved, meaning pi times 7 squared times 15 equals 2 times pi times radius squared times 7.5. Simplifying this gives 49 times 15 equals 15 times radius squared, so radius squared equals 49. Taking the square root gives the radius as 7 cm.

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