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 height of 3.5 feet. 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.
THANK YOU!!
all: 2*2.5^2 + 4*2.5*3.5
to exclude the bottom, subtract 2.5^2 from that total.
now compare in whatever way you want.
sum1 tell me the answer
tysm
To compare the amount of paint required to paint all but the bottom surface of the prism with the amount required to paint the entire prism, we need to calculate the surface areas of each.
To paint all but the bottom surface, we need to calculate the surface area of the four vertical sides of the rectangular prism.
The surface area of a rectangular prism is given by the formula:
2 * (length * width + length * height + width * height)
In this case, the length and width of the base are both 2.5 feet, and the height is 3.5 feet.
Surface area of all but the bottom surface:
= 2 * (2.5 * 2.5 + 2.5 * 3.5 + 2.5 * 3.5)
= 2 * (6.25 + 8.75 + 8.75)
= 2 * (23.75)
= 47.5 square feet
To calculate the amount of paint needed for the entire prism, we need to calculate the surface area of all six faces.
Surface area of the entire prism:
= 2 * (2.5 * 2.5 + 2.5 * 3.5 + 2.5 * 3.5) + 2.5 * 2.5
= 2 * (6.25 + 8.75 + 8.75) + 6.25
= 2 * (23.75) + 6.25
= 47.5 + 6.25
= 53.75 square feet
Therefore, Enya would use 47.5 square feet of paint to paint all but the bottom surface of the prism and 53.75 square feet of paint to paint the entire prism.