A solid lies between planes perpendicular to the x-axis at x = -11 and x = 11. The cross-sections perpendicular to the x-axis between these planes are squares whose bases run from the semicircle

y =

-√√121-x²₁

to the semicircle y =√121-x². Find the volume of the solid.

The volume of the solid is

(Simplify your answer.)

cubic units.