**Question:** Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.

**Solution:** Let be the radius of the circular base and be the height of closed right circular cylinder.

Formula for Total surface area

–(i)

Volume of cylinder

Differentiating with respect r

And

For max and minima

.

Since

Hence volume of cylinder is max when

Value of S putting in equation (i)

Height of cylinder = Diametre of cylinder

Hence volume of cylindr is max when

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