A cylinder with a volume of 72 is described around a sphere. find the volume of the ball.

What does it mean that the cylinder is described around the ball? This means that the ball, located inside the cylinder, touches the bases and walls of the cylinder, that is, the radius of the ball coincides with the radius of the base of the cylinder, and the height of the cylinder is equal to the diameter of the ball or two radii. Let us recall the fundamental formulas describing the volume of a ball and the volume of a cylinder:

Vcylinder = Sokr * h = n * R ^ 2 * h.

Vball = 4 * n * R ^ 3/3.

Taking into account the above features, the volume of a cylinder can be written as follows:

Vcylinder = n * R ^ 2 * h = 2 * n * R ^ 3 = 72;

n * R ^ 3 = 72/2 = 36.

Then the volume of the ball will be:

Vball = 4 * n * R ^ 3/3 = 4 * 36/3 = 48.

Unfortunately, the example does not specify units of measurement, so we can only clarify that the units in which the volume is measured are always cubed.

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