Multiple choice

A solid cylinder of glass whose diameter is 1.5 m and height 1 m is melted an recasted into a sphere then the radius of the sphere is

  1. 1 m

  2. 0.75 m

  3. 1.25 m

  4. 1.5 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * (0.75)^2 * 1 = 0.5625 * pi. Volume of sphere = 4/3 * pi * R^3. 4/3 * R^3 = 0.5625. R^3 = 0.5625 * 3 / 4 = 0.421875. R = cube root(0.421875) = 0.75.

AI explanation

Using the volume conservation principle when melting and recasting, the volume of the sphere equals the volume of the original cylinder. The volume of the cylinder is pi multiplied by the square of the radius multiplied by the height, which is pi multiplied by 0.75 squared multiplied by 1. Setting this equal to the sphere volume formula gives 4 divided by 3 multiplied by pi multiplied by the sphere radius cubed equals pi multiplied by 0.5625. Solving for the sphere radius yields a value of 0.75 m.

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