The ball is inscribed in the cylinder, the volume of the cylinder is 60, find the volume of the ball.
| May 14, 2021 | education
Since the ball is inscribed in a cylinder, the height of the cylinder is equal to the diameter of the circle at the base of the cylinder and the diameter of the ball.
The volume of the cylinder is: Vcyl = Sosn * h = n * R ^ 2 * h.
Since h = 2 * R, then Vcyl = n * R ^ 2 * 2 * R = 2 * n * R ^ 3 = 60. (1).
The volume of the ball can be determined by the formula:
Vball = 4 * n * R ^ 3/3 = (2 * n * R ^ 3) * 2/3.
Substitute equation 1 in the last expression.
Vball = Vcyl * 2/3 = 60 * 2/3 = 40 cm3.
Answer: The volume of the ball is 40 cm3.
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