Multiple choice

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Height of the resultant cylinder would be:

  1. 110 cm

  2. 3.84 cm

  3. 30 cm

  4. 2.74 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of sphere = (4/3)pi(4.2)^3. Volume of cylinder = pi*(6)^2*h. (4/3)*(4.2)^3 = 36*h. h = (4 * 74.088) / (3 * 36) = 296.352 / 108 = 2.744 cm.

AI explanation

Because the metallic sphere is melted and recast, the volumes are conserved. Using the volume formulas, four thirds pi times 4.2 cubed equals pi times 6 squared times the height. Solving for the height gives 4.2 cubed divided by 9, which is 74.088 divided by 9, resulting in a height of 2.74 cm.

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