Find the maximum volume of a cylindrical soda can such that the sum of its height and its circumference is 120 cm.

The maximum volume of cylinder is 20371.83 cm³.

Let us consider that, radius of cylinder is r and height is h .

Volume of cylinder is,

Since, the sum of its height and its circumference is 120 cm.

So,    

Substituting value of h in volume equation of cylinder.

For maximum volume, differentiate above expression with respect to r and equate with zero.

So, radius of cylinder is,  

Now,  

Substituting value of r and h in volume formula of cylinder.

Value of

Thus, the maximum volume of cylinder is 20371.83 cm³.

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