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?
(2 points)
Responses
$160
$160
$48
$48
$80
$80
$96
First, we need to calculate the surface area of the rectangular prism doghouse.
Assuming the dimensions of the rectangular prism are:
Length = L
Width = W
Height = H
Surface Area of a Rectangular Prism = 2lw + 2lh + 2wh
Substitute L = length of the rectangular prism, W = width of the rectangular prism, and H = height of the rectangular prism:
Surface Area = 2(LW + LH + WH)
Since we are making an opening for the doghouse, we need to subtract the area of the piece cut out. If the opening has dimensions x (width) and y (height), then the area of the cut-out piece would be xy.
Total surface area = Surface Area - xy
Given that plywood costs $2 per square foot, we can calculate the total cost:
Total Cost = Total Surface Area * Cost of Plywood
Total Cost = (2(LW + LH + WH) - xy) * 2
Now, substitute the known values to find the total cost. Without specific dimensions provided, we can't calculate the exact total cost.