What fraction of the volume of the cylinder is the volume of the sphere?

2/3
Note : The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.

How do you find the volume of a cylinder inscribed in a sphere?

Let R be the radius of the sphere and let h be the height of the cylinder centered on the center of the sphere. By the Pythagorean theorem, the radius of the cylinder is given by r2=R2−(h2)2. The volume of the cylinder is hence V=πr2h=π(hR2−h34).

What is the maximum volume of a cylinder inscribed in a sphere?

As it is clear from the figure below that the radius of the sphere = r cm, radius of the cylinder =R cm and the height of the cylinder = h cm. Hence, the volume of the largest cylinder that can be inscribed in a sphere of radius $3\sqrt 3 $ cm is $108 cm^3$.

What is 4/3 in the volume of a sphere?

The formula for the volume of a sphere is V = 4/3 πr³. See the formula used in an example where we are given the diameter of the sphere. Created by Sal Khan and Monterey Institute for Technology and Education.

What is the volume of a box that can be inscribed in a sphere of unit radius?

The maximal volume of the rectangle inside the sphere of radius r and that volume is 8r3/3√3.

Why is a sphere 2/3 of a cylinder?

If the height of the cylinder equals the diameter of the sphere, , and if the diameter of the cylinder is equal to the diameter of the sphere, , so the volume is . This is half as much again as the volume of the sphere, which is two-thirds of the volume of the cylinder.

Why is the sphere Formula 4 3?

Since the cylinder/cone and hemisphere have the same height, by Cavalieri’s Principle the volumes of the two are equal. The cylinder volume is πR3, the cone is a third that, so the hemisphere volume is 23πR3. Thus the sphere of radius R has volume 43πR3.

What is the volume of a unit sphere?

The formula for the volume of a sphere is V = 4/3 πr³.