Multiple choice

A solid metallic hemisphere of radius 6.3 cm is melted and recast into a right circular cylinder of radius 9 cm. What is the height (in cm, correct to one decimal place) of the cylinder?

  1. 1.9

  2. 2.1

  3. 2.7

  4. 2.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * pi * (6.3)^3. Volume of cylinder = pi * R^2 * h = pi * 9^2 * h. Equating them: (2/3) * (6.3)^3 = 81 * h. h = (2 * 250.047) / (3 * 81) = 500.094 / 243 = 2.058. Rounding to one decimal place gives 2.1.

AI explanation

Because the hemisphere is melted and recast, the volume of the cylinder equals the volume of the hemisphere, given by the formula (2/3) times pi times the radius cubed. Substituting the radius of 6.3 cm gives a volume of approximately 523.91 cm3. Setting this equal to the cylinder's volume formula, pi times 9 squared times the height, we solve to find the height is 2.1 cm.

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