Multiple choice

A cylinder having diameter 32 cm and height 4 cm is melted to make 24 spheres out of it of the same size. Find out the radius of each sphere.

  1. 3.1 cm

  2. 4.17 cm

  3. 3 cm

  4. 3.17 cm

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 16^2 * 4 = 1024 * pi. Volume of 24 spheres = 24 * (4/3) * pi * r_s^3 = 32 * pi * r_s^3. Equating them: 1024 * pi = 32 * pi * r_s^3, so r_s^3 = 32, r_s = cube root of 32, which is approximately 3.1748 cm.

AI explanation

The volume of the cylinder is pi times radius squared times height, which equals pi times 16 squared times 4, or 1024 times pi. The total volume of the 24 spheres is 24 times four thirds times pi times radius cubed, which is 32 times pi times radius cubed. Equating the volumes gives 1024 times pi equals 32 times pi times radius cubed, so radius cubed is 32 and the radius is the cube root of 32. This value is approximately 3.17 cm. The correct answer is 3.17 cm.

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