Answer
$88 \pi \approx 276 \space in^{3}$
Work Step by Step
We need to integrate the integral as shown below:
$Volume = \int_{-11/2}^{11/2} ( \pi) \sqrt {12(1-\dfrac{4x^2}{121})} dx\\= (12 \pi) [x-\dfrac{4x^3}{363} ]_{-11/2}^{11/2} \\=(132 \pi) [1-\dfrac{1}{3}] \\= 88 \pi \\ \approx 276 \space in^{3}$
