Calculate the volume of the ball inscribed in the cylinder, the diagonal of the axial section

Calculate the volume of the ball inscribed in the cylinder, the diagonal of the axial section of which is equal to 10√2.

Since a ball is inscribed in the cylinder, the height of the BC cylinder is equal to the diameter of the ball OO1, and then the axial section of the cylinder will have the shape of a square.

Knowing the diagonal of the square, we determine the length of its side. AC ^ 2 + BC ^ 2 = AB ^ 2 = (10 * √2) ^ 2 = 200.

2 * AC ^ 2 = 200.

AC ^ 2 = 100.

AC = 10 cm.

The height of the cylinder and the diameter of the ball are 10 cm.Then the radius of the ball OA = R = OO1 / 2 = 10/2 = 5 cm.

Let’s define the volume of the ball.

Vball = 4 * n * R ^ 3/3 = 4 * n * 125/3 = 500 * n / 3 cm3.

Answer: The volume of the ball is 500 * p / 3 cm3.