Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is. Also find the maximum volume.

Open in App

Solution

A sphere of fixed radius (R) is given.

Let r and h be the radius and the height of the cylinder respectively.

From the given figure, we have

The volume (V) of the cylinder is given by,

Now, it can be observed that at.

∴The volume is the maximum when

When, the height of the cylinder is

Hence, the volume of the cylinder is the maximum when the height of the cylinder is.

Suggest Corrections

Similar questions

Q. Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is . Also find the maximum volume.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is $\frac{2 R}{\sqrt{3}}$ . Also, find the maximum volume.

Q. Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius

20 c m

\frac{40}{\sqrt{3}} c m

.Also find the maximum volume.

Q. Show that the height of the cylinder of maximum volume, that can be inscribed in a sphere of radius R is

\frac{2 R}{\sqrt{3}}

Also find the maximum volume.

Q. Prove that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius

R

\frac{2 R}{\sqrt{3}}

. Also find the maximum volume.

Join BYJU'S Learning Program