x ^2 + y ^2 = 9 => y = y(x) = ± √(9 - x ^2)
Each cross section would be a square with side length equal to the vertical distance between the upper and lower semicircles defined by y(x), which is
√(9 - x ^2) - (- √(9 - x ^2)) = 2 √(9 - x ^2)
The area of each square section is the square of this length,
(2 √(9 - x ^2)) = 4 (9 - x ^2) = 36 - 4x ^2
We get the whole solid for -3 ≤ x ≤ 3, so integrating gives a volume of
[tex]\displaystyle\int_{-3}^3(36-4x^2)\,\mathrm dx=\boxed{144}[/tex]
