Answer:
A) 166 ft²
B) 4 cans
Step-by-step explanation:
Part A
The doghouse can be modelled as a rectangular prism.
To find the surface area of the doghouse, we can use the formula for the surface area of a rectangular prism:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Surface area of a Rectangular Prism}}\\\\SA=2(wl+hl+hw)\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$w$ is the width of the base.}\\ \phantom{ww}\bullet\;\textsf{$l$ is the length of the base.}\\ \phantom{ww}\bullet\;\textsf{$h$ is the height of the prism.}\end{array}}[/tex]
In this case:
w = 5 ft
l = 7 ft
h = 4 ft
Substitute the given values into the surface area formula and solve for SA:
[tex]SA=2(5 \cdot 7+4 \cdot 7+4 \cdot 5) \\\\SA=2(35+28+20) \\\\SA=2(83) \\\\SA=166\; \sf ft^2[/tex]
Therefore, the total surface area of the doghouse is:
[tex]\Large\boxed{\boxed{\textsf{Total surface area}=166\; \sf ft^2}}[/tex]
[tex]\dotfill[/tex]
Part B
To determine how many cans of paint are needed to paint the doghouse, divide the total surface area by the coverage of one can of paint:
[tex]\textsf{Number of cans} = \dfrac{\textsf{Total surface area}}{\textsf{Coverage per can}} \\\\\\ \textsf{Number of cans} = \dfrac{166 \textsf{ ft}^2}{50 \textsf{ ft}^2/\textsf{can}} \\\\\\ \textsf{Number of cans} = 3.32[/tex]
Since we can't purchase a fraction of a can, we need to round up to the nearest whole number. Therefore, the number of cans of paint needed to paint the doghouse is:
[tex]\Large\boxed{\boxed{\textsf{Number of cans}=4}}[/tex]
