A metal cylinder with a base diameter d = 4 cm and a height h = 4 cm was remelted into a ball. Calculate the radius of this ball.

univerkov | June 18, 2021 | education

Determine the radius of the metal cylinder. R = AD / 2 = 4/2 = 2 cm.

Determine the area of the base of the cylinder. Sb = π * R ^ 2 = 4 * π cm2.

Let’s calculate the volume of the cylinder. V = Ssc * AB = 4 * π * 4 = 16 * π cm3.

Since the volume of the resulting ball is equal to the volume of the cylinder, the volume of the ball is: Vsh = 16 * π = 4 * π * R ^ 3/3.

R3 = 16 * π * 3/4 * π = 12.

R = 3√12 cm.

Answer: The radius of the ball is 3√12 cm.

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