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6 September, 00:18

20. Short Response A company is experimenting with two new boxes for packaging merchandise. Each box is a cube with the side lengths shown. What is the ratio of the surface area of the smaller box to the surface area of the larger box?

Large box = 18in

Small box=12in

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  1. 6 September, 01:40
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    We are tasked to solve for the ratio of the two boxes. Boxes are cubes. We can use the formula in solving the surface area of the box as shown below:

    Surface Area of Cube = 6a² where "a" is the length of the side.

    For smaller box:

    Area = 6 (12) ²=864

    Area = 864

    For the larger box:

    Area = 6 (18) ²

    Area=1944

    Then, the ratio is:

    Area smaller box/Area larger box = 864/1944

    Ratio=4:9
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