Answer
$ 88 \pi $ or, $\approx 276 \space in^{3}$
Work Step by Step
We need to use the shell model as follows:
$V=\int_p^{q} (2 \pi) \cdot (\space radius \space of \space shell) ( height \space of \space Shell) \space dx$
$ \implies V= \int_{-11/2}^{11/2} ( \pi) \sqrt {12(1-\dfrac{4x^2}{121})} dx$
or, $=12 \pi \times [x-\dfrac{4x^3}{363} ]_{-11/2}^{11/2}$
or, $=132 \pi [1-\dfrac{1}{3}]$
or, $= 88 \pi $ or, $\approx 276 \space in^{3}$
