Marianna is painting a ramp for the school play that is in the shape of a right triangular prism. The ramp has the dimensions shown. She will not pain

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asked 2020-11-20
Marianna is painting a ramp for the school play that is in the shape of a right triangular prism. The ramp has the dimensions shown. She will not pain the back or bottom surfaces of the ramp.
Each can of paint covers 1,000 square inches. What is the fewest number of full cans of paint Marianna will need? Circle the minimum number of cans.

Answers (1)

Since Marianna will not paint the back or the bottom surfaces of the ramp, she will only paint the rectangular face on top and the two triangular faces on the sides.
The rectangular face has dimensions of 59.5 inches by 50 inches so its area is 59.5(50)=2975 square inches.
The triangular faces have dimensions of 14 inches by 48 inches so each one has an area of \(\displaystyle{\frac{{{1}}}{{{2}}}}{\left({48}\right)}{\left({14}\right)}={24}{\left({14}\right)}={336}\) square inches.
The total area that Marianna will paint is then 2975+2(336)=2975+672=3647 square inches.
Since each can covers 1,000 square inches and \(\displaystyle{\frac{{{3647}}}{{{1000}}}}={3.647}\), then she will need 4 full cans of paint to have enough paint.
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