Question

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 3.5 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.

Answer 1

To compare the amount of paint needed to paint all but the bottom surface of the cupboard to the amount needed to paint the entire cupboard, calculate the surface area of each

Step-by-step explanation:

To compare the amount of paint Enya would use to paint all but the bottom surface of the cupboard with the amount she would use to paint the entire cupboard, we need to calculate the surface area of each.

The surface area of the entire cupboard is the sum of the area of the six faces of the rectangular prism. The area of each face can be calculated by multiplying its length and width. So, the surface area of the entire cupboard is 2(2.5 ft x 3.5 ft) + 2(2.5 ft x 2.5 ft) + 2(3.5 ft x 2.5 ft).

The surface area of all but the bottom surface of the cupboard is the same as the surface area of the entire cupboard minus the area of the bottom face. So, the surface area of all but the bottom surface is 2(2.5 ft x 3.5 ft) + 2(2.5 ft x 2.5 ft).

Answer 2

The amount of paint required to paint the whole cupboard is:


`2*2.5^2+4*(2.5*3.5) \\=47.5 ft^2`

The amount of paint required to paint all but the bottom surface is:


`2.5^2 + 4(2.5*3.5) \\= 41.25 ft^2`

So the difference in paint required is 6.25 square feet worth of paint.