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A student is painting a doghouse like the rectangular prism shown.

Part A: Find the total surface area of the doghouse. Show your work.

Part B: if one of paint will cover 50 square feet how many cans of paint are needed to paint the doghouse? Explain.

A Student Is Painting A Doghouse Like The Rectangular Prism Shown Part A Find The Total Surface Area Of The Doghouse Show Your Work Part B If One Of Paint Will class=

Sagot :

semsee45

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]

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