Multiple choice

What is the height of a cylinder that has the same volume and radius as a sphere of diameter 12 cm?

  1. 7 cm

  2. 10 cm

  3. 9 cm

  4. 8 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sphere diameter = 12, so radius = 6. Volume = (4/3) * pi * 6^3 = 288 * pi. Cylinder volume = pi * r^2 * h = pi * 6^2 * h = 36 * pi * h. Equating: 36 * pi * h = 288 * pi, so h = 8.

AI explanation

The sphere has a radius of r = 12 / 2 = 6 cm, so its volume is 4/3 * pi * r^3 = 4/3 * pi * 216 = 288 pi. Setting this equal to the cylinder's volume formula, pi * r^2 * h, we get pi * 36 * h = 288 pi. Solving for h gives h = 8 cm.

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