Given:
The sum of the radius and height of the cylinder is 9 units.
To find the largest volume:
Since sum of the radius and height of the cylinder is 9 units.

The formula of volume of the cylinder is,

To find the maximum of the function:
Differentiate with respect to r,

It is impossible that r=0.
So, let us substitute r=6 in equation (2) we get,

Hence, the largest volume of the cylinder is 339.43 cubic units.