Multiple choice

The radius of the sphere and the radius of the base of the right circular cylinder are each 3 cm. If their volumes are equal, then the height (in cm) of the cylinder is

  1. 4 cm

  2. 9 cm

  3. 12 cm

  4. 22 cm
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A Correct answer
Explanation

Volume of sphere = 4/3 * pi * r^3 = 4/3 * pi * 27 = 36 * pi. Volume of cylinder = pi * r^2 * h = pi * 9 * h. 36 * pi = 9 * pi * h, so h = 4.

AI explanation

Using the formula for the volume of a sphere, V = (4/3)πr³, we get (4/3) × π × 3³ = 36π cubic centimeters. Setting this equal to the cylinder's volume, V = πr²h, we have π × 3² × h = 36π. Solving for h gives 9h = 36, so the height of the cylinder is 4 cm.

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