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 cardboa

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.

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Isabella 1 week 2021-11-25T17:54:49+00:00 1 Answer 0 views 0

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    2021-11-25T17:56:01+00:00

    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,

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