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 \:in^2`

Explanation:

Volume of the butter in the cardboard = 31.25 cubic inches

Length of the Molded Square Prism =5 Inches

Let the length of the square cross sectional area = x

Volume of the Prism
`=x^2l`

Since l=5 Inches

`5x^2=31.25\\x^2=6.25\\x=2.5\: Inches`

Next, we determine the surface area of the New Cardboard box to be made.

Length of the Cardboard Box=5 Inches

Length of the square cross sectional area = 2.5 Inches

Total Surface Area
`=2(x^2+xl+xl)=2(x^2+2xl)`

`=2(2.5^2+2(2.5)(5))\\=2(6.25+25)\\=2*31.25\\=62.5 \:in^2`

Therefore,
`62.5 \:in^2` of cardboard is needed,