By 3-4-5 triangle

$x = 4 ~ \text{in.}$

$h_1 = 2x = 8 ~ \text{in.}$

$h_2 = \frac{1}{2}(10 - h_1) = 1 ~ \text{in.}$

Volume cut out

$V = V_{cylinder} + 2V_{segment}$

$V = \pi(3^2)(h_1) + 2 \times \dfrac{\pi{h_2}^2}{3} [ \, 3(5) - h_2 \, ]$

$V = \pi(3^2)(8) + \dfrac{2\pi (1^2)}{3} [ \, 3(5) - 1 \, ]$

$V = \frac{244}{3}\pi ~ \text{in.}^3 = 255.52 ~ \text{in.}^3$ *answer*