A ball is inscribed in the cylinder so that the bases of the cylinder touch the ball.
| May 3, 2021 | education
A ball is inscribed in the cylinder so that the bases of the cylinder touch the ball. The volume of the ball is V. Find the volume of the cylinder.
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 ball is: Vball = 4 * n * R ^ 3/3 = V cm3.
Then n * R ^ 3 = V * 3 / 4. (1).
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 * R3
Substitute equation 1 in the last expression.
Vcyl = 2 * V * 3/4 = 3 * V / 2 cm3.
Answer: The volume of the cylinder is 3 * V / 2 cm3.
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