The volume of a sphere is given by the formula (4/3)πr³, where r is the radius of the sphere. The volume of a cylinder is given by the formula πr²h, where r is the radius and h is the height of the cylinder.

In this case, the sphere fits exactly into the cylinder, so the height of the cylinder is equal to the diameter of the sphere, or 2r.

So, the volume of the cylinder is πr²(2r) = 2πr³.

The fraction of the cylinder's volume that the sphere takes up is therefore (4/3)πr³ / 2πr³ = 2/3.

So, the sphere takes up 2/3 of the volume of the cylinder.

Question

The volume of a sphere is given by the formula (4/3)πr³, where r is the radius of the sphere. The volume of a cylinder is given by the formula πr²h, where r is the radius and h is the height of the cylinder.

In this case, the sphere fits exactly into the cylinder, so the height of the cylinder is equal to the diameter of the sphere, or 2r.

So, the volume of the cylinder is πr²(2r) = 2πr³.

The fraction of the cylinder's volume that the sphere takes up is therefore (4/3)πr³ / 2πr³ = 2/3.

So, the sphere takes up 2/3 of the volume of the cylinder.

Knowee AI · Accepted Answer

The volume of a sphere is given by the formula (4/3)πr³, where r is the radius of the sphere. The volume of a cylinder is given by the formula πr²h, where r is the radius and h is the height of the cylinder.

In this case, the sphere fits exactly into the cylinder, so the height of the cylinder is equal to the diameter of the sphere, or 2r.

So, the volume of the cylinder is πr²(2r) = 2πr³.

The fraction of the cylinder's volume that the sphere takes up is therefore (4/3)πr³ / 2πr³ = 2/3.

So, the sphere takes up 2/3 of the volume of the cylinder.

A sphere fits exactluy into a cylinder, the sphere is touching both circular faces of the cylinder. What fraction of the cylinder's volume does the sphere take up?

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