011 Review Problem - Cutting the strongest square timber

$x^2 + x^2 = 2^2$

$2x^2 = 4$

$x^2 = 2$
 

$V_{waste} = V_{log} - V_{timber}$

$V_{waste} = \frac{1}{4}\pi d^2 L - x^2 L$

$V_{waste} = \frac{1}{4}\pi (2^2)(8) - 2(8)$

$V_{waste} = 9.1327 ~ \text{ft.}^3$           answer