Multiple choice

A metallic sphere of radius 4 cm is melted and re-caste into a cylinder, whose radius is 4/3 cm. What is the height of the cylinder?

  1. 44 cm

  2. 48 cm

  3. 66 cm

  4. 98 cm

  5. 40 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of sphere = 4/3 * pi * 4^3 = 256/3 * pi. Volume of cylinder = pi * (4/3)^2 * h = 16/9 * pi * h. Equating them: 256/3 = 16/9 * h. h = (256/3) * (9/16) = 16 * 3 = 48 cm.

AI explanation

When a solid is melted and recast, its total volume remains constant. The volume of a sphere is 4/3 * pi * r^3, so the volume of the metallic sphere is 4/3 * pi * 4^3 = 256/3 * pi cubic cm. The volume of the resulting cylinder is pi * r^2 * h = pi * (4/3)^2 * h = 16/9 * pi * h. Equating the two volumes gives 16/9 * pi * h = 256/3 * pi. Solving for the height gives h = (256/3) / (16/9), which simplifies to h = 48 cm.

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