## Tin drum: Maximize volume

Say we have a square tin sheet with side lenght $a$. We want to cut out a circle and a rectangle in order to construct an oil drum. What is the largest volume the finished oil drum can have with this setup? (Remember: The rectangle and the circle to be cut out of the tin sheet may not overlap.)

I got $V_{MAX}=\frac{\pi}{27}a^3$

Can someone please check if this is correct?

Thanks for any help.