Enya is building a storage cupboard in the shape of a rectangular prism. The rectangular prism has a square base with side lengths of 2.5 feet and a height of 3.6 feet. Use percentage to compare the amount of paint she would use to paint all but the bottom surface of the prism to the amount she would use to paint the entire prism. Round your final answer to the nearest tenth.
Assuming that the amount of paint used is proportional to the surface area painted, and
assuming that she paints of 6 surfaces of the prism,
total surface area = 2( (2.5)(2.5) + (2.5)(3.6) + (2.5)(3.6) ) = ....
the area of the base = (2.5)^2 = ....
subtract the two answers
form the fraction: surface without bottom/total surface area
convert that to a percentage.
Let me know what you get
To compare the amount of paint Enya would use to paint all but the bottom surface of the prism to the amount she would use to paint the entire prism, we need to find the area of each surface and then calculate the percentage.
First, let's find the area of each surface:
- Base surface: Since it is a square, the area is calculated by multiplying the length of one side by itself. So, the area of the base surface is 2.5 * 2.5 = 6.25 square feet.
- Side surfaces: Since the prism is rectangular, the area of each side surface is calculated by multiplying the length of one side by the height. So, the area of each side surface is 2.5 * 3.6 = 9 square feet.
- Total area of the side surfaces: Since there are four side surfaces in a rectangular prism, the total area of all side surfaces is 4 * 9 = 36 square feet.
Now, let's calculate the amount of paint Enya would use to paint all but the bottom surface of the prism:
- Total area of the prism excluding the bottom surface: This is calculated by subtracting the area of the base surface from the total area of all surfaces. So, the total area of the prism excluding the bottom surface is 36 - 6.25 = 29.75 square feet.
Finally, let's calculate the percentage of paint Enya would use to paint all but the bottom surface of the prism compared to the amount she would use to paint the entire prism:
- Percentage: This is calculated by dividing the area of the prism excluding the bottom surface by the total area of the prism and then multiplying by 100. So, the percentage is (29.75 / 36) * 100 = 82.6%.
Rounding the final answer to the nearest tenth, Enya would use around 82.6% of the paint to paint all but the bottom surface of the prism compared to the amount she would use to paint the entire prism.