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Advanced Math/Dimensions, Board Feet Follow-up


That is the complete problem. I am assuming it would be a cuboid.

It was asking for the largest square piece, but like you said, it could not be square.

Also, I read that a timber is 5" wide or wider.

Is there a solution possible from the added information ?

Thanks again.

"A circular log is 2 feet in diameter. Determine to the nearest inch, the largest square piece of timber that can be cut from the log."
I assume the sides of the log will be removed to form a cuboid:

Consider a cross-section of the log with an inscribed square.
diagonal of square = diameter of circle = 2 ft
By the Pythagorean Theorem, each side of the square is √2 ft.
√2 ft × 12 inches/ft ≅ 17 inches
The largest square piece of timber will be 17 inches by 17 inches.
"Determine number of board feet in the timber if it is 12 feet in length, with no allowances for waste."
Well, I learned something new today: 1 board ft = 144 in³.
12 ft × 12 inches/ft = 144 in
volume of timber = 17×17×144 in³ = 289×144 in³ × 1 board ft/(144 in³) = 289 board ft

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