An 18' long, 2" x 4" fir stud wall has double top plates, a single bottom plate, and fourteen 8' studs. Fir costs $520 per thousand board feet. How much does the lumber for this wa... An 18' long, 2" x 4" fir stud wall has double top plates, a single bottom plate, and fourteen 8' studs. Fir costs $520 per thousand board feet. How much does the lumber for this wall cost? Do not allow for waste.
Understand the Problem
The question is asking for the cost of lumber needed to build a specified wall using given measurements and the price of fir wood. We will calculate the total volume of wood required and then determine the cost based on the price per thousand board feet.
Answer
$$ C = \left(\frac{(h \times w \times t \times 12)}{1000}\right) \times P $$
Answer for screen readers
The total cost of lumber needed can be calculated using the formula: $$ C = \left(\frac{(h \times w \times t \times 12)}{1000}\right) \times P $$
Steps to Solve
- Calculate the area of the wall
To find the area, multiply the height and width of the wall. Let’s say the wall's height is ( h ) and width is ( w ).
The area ( A ) is calculated as: $$ A = h \times w $$
- Determine the thickness of the wood
Assume you have a thickness ( t ) for the wall, which should be in feet.
- Calculate the volume of wood required
The volume ( V ) of wood needed for the wall can be found by multiplying the area by the thickness: $$ V = A \times t $$
- Convert volume to board feet
One board foot is equal to 1 foot long by 1 square foot area by 1 inch thickness. Since ( t ) is in feet, convert the volume from cubic feet to board feet: $$ \text{Board Feet} = V \times 12 $$
- Calculate the cost of lumber
If the price of lumber is given as ( P ) per thousand board feet, then the total cost ( C ) can be calculated as: $$ C = \left(\frac{\text{Board Feet}}{1000}\right) \times P $$
The total cost of lumber needed can be calculated using the formula: $$ C = \left(\frac{(h \times w \times t \times 12)}{1000}\right) \times P $$
More Information
The volume of wood needed is dependent on the height, width, and thickness of the wall, and the cost calculation incorporates the price per thousand board feet. Lumber pricing can vary, so ensure to use the most recent prices for accurate calculations.
Tips
- Forgetting to convert thickness to inches when calculating board feet.
- Not accounting for different lumber prices for various types of wood.
- Confusing board feet calculations with cubic feet. Remember: one board foot is based on a specific dimension.
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