Question

A cardboard box holds 31.25 cubic inches of creamy butter. The butter is molded into a square prism that is 5 inches long. How much cardboard would it take to make the box, assuming the butter fits exactly into the box and there is no overlap.

Answer 1

62.5 Square Inches

Explanation:

Volume of the molded butter=31.25 cubic inches

Length of the molded butter=5 Inches

Volume=length X width X height

Since it is a square prism, width = height. Therefore:

`31.25=5w^2\\`

Divide both sides by 5

`w^2=6.25\\w=√(6.25)=2.5 \:inches`

The amount of cardboard needed to make the box, which exactly fits the butter is the total surface area of the butter.

Total Surface area
`=2(lw+lw+w^2) =4lw+2w^2`

Since l=5 in, w= 2.5 in

Surface Area
`=4*5*2.5+2(2.5)^2`

=62.5 Square Inches