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

Answer:

$62.5 \:in^2$

Step-by-step 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,