Multiple choice

If the height and diameter of a right circular cylinder are 32 cm and 6 cm respectively, then the radius of the sphere whose volume is equal to the volume of the cylinder is

  1. 3 cm

  2. 4 cm

  3. 6 cm

  4. None
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C Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 3^2 * 32 = 288pi. Volume of sphere = 4/3 * pi * R^3 = 288pi. R^3 = 288 * 3 / 4 = 216. R = 6.

AI explanation

The volume of the right circular cylinder is pi times r squared times h, so using the radius 3 cm and height 32 cm gives pi times 9 times 32, which is 288 times pi. Equating this to the volume of the sphere, 4 over 3 times pi times R cubed, yields 288 times pi equals 4 over 3 times pi times R cubed. Solving for R gives R cubed equals 216, meaning the radius of the sphere is 6 cm.

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