A woodworker is purchasing solid oak lumber to construct a tabletop. The bill of materials… — Armed Services Vocational Aptitude Battery (ASVAB)

A woodworker is purchasing solid oak lumber to construct a tabletop. The bill of materials calls for $5$ boards, each measuring a nominal $2\text{ inches}$ thick, $9\text{ inches}$ wide, and $8\text{ feet}$ long. What is the total volume of lumber needed, expressed in board feet?

Answer: 60 board feet

Answer

The total volume of lumber required is

60\text{ board feet}

One board foot is defined as

1\text{ in} \times 12\text{ in} \times 1\text{ ft} = 144\text{ in}^3

. Using the standard formula

\text{Board Feet} = \frac{\text{Thickness (in)} \times \text{Width (in)} \times \text{Length (ft)}}{12}

, each board contains

\frac{2 \times 9 \times 8}{12} = 12\text{ board feet}

. Multiplying by

5

pieces yields a total of

60\text{ board feet}

Step-by-Step Solution

Calculate the board feet contained in one board using nominal thickness and width in inches and length in feet.

\text{Board Feet per piece} = \frac{2\text{ in} \times 9\text{ in} \times 8\text{ ft}}{12} = \frac{144}{12} = 12\text{ board feet}

One board foot represents the volumetric equivalent of a board

1\text{ inch}

thick,

12\text{ inches}

wide, and

1\text{ foot}

long (or

144\text{ cubic inches}

). Dividing by

12

converts inch-inch-foot dimensions directly to board feet.

Multiply the volume per board by the total quantity of boards.

\text{Total Board Feet} = 12\text{ board feet} \times 5 = 60\text{ board feet}

The project requires

5

identical boards of specified dimensions.

Key Concept

Calculation of board footage for dimensional lumber using nominal dimensions and the standard volume formula.

Estimated Time:1m 0s

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