Problem 11 Find the waste in cutting the strongest square timber from a circular log of uniform diameter 2 ft. and length 8 ft.

Solution 11

$2x^2 = 4$

$x^2 = 2$

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

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

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

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

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