Mr. Richardson is building a doghouse out of plywood in the shape of a rectangular prism. The piece he cuts out for the opening of the doghouse will be used to make a sign. Plywood costs $2 per square foot. What is the total cost of the plywood Mr. Richardson needs for the doghouse?
To find the total cost of the plywood Mr. Richardson needs for the doghouse, we first need to calculate the surface area of the rectangular prism.
Let's assume the dimensions of the doghouse are:
Length = L
Width = W
Height = H
The surface area of a rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Since the piece cut out for the opening will be used to make a sign, we need to subtract the area of the opening from the total surface area.
Let's assume the dimensions of the opening are:
Length = l
Height = h
The area of the opening is given by:
Area = lh
So, the total surface area of the plywood needed for the doghouse without the opening is:
Total Surface Area = 2lw + 2lh + 2wh - lh
Total Surface Area = 2lw + 2lh + 2wh - lh
The total cost of the plywood can be calculated by multiplying the total surface area by the cost per square foot:
Total Cost = Total Surface Area * $2
Once the dimensions of the doghouse are known, the values can be substituted into the formula to find the total cost of the plywood.