Volume of a football!

If the American NFL regulation football

有一个尖端,tip length of $11$inches and a largest round circumference of $22$in the middle, then the volume of the American football is $\text{\_\_\_\_\_\_\_\_\_\_\_\_}.$

Note: The American NFL regulation football is not an ellipsoid. The long cross-section consists of two circular arcs meeting at the tips. Don't use the volume formula for an ellipsoid.

Answer is in cubic inches.