Question
4) In math class, Abby learned that the ratio between the surface area of a cube and the area of one side is 6 to 1 . When Abby got a cube-shaped box in the mail, she decided to test this fact. The area of one side of the box was 20 square inches. 4) What was the surface area of the entire box?
Ask by Floyd Tran. in the United States
Dec 17,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The surface area of the entire box is 120 square inches.
Solution
To find the surface area of the entire box, we can use the ratio given in the problem. The ratio of the surface area of a cube to the area of one side is 6 to 1. This means that if the area of one side is \( A \), then the surface area \( S \) can be expressed as:
\[
S = 6A
\]
In this case, the area of one side of the box is given as 20 square inches. We can substitute this value into the equation:
\[
S = 6 \times 20
\]
Calculating this gives:
\[
S = 120 \text{ square inches}
\]
Therefore, the surface area of the entire box is \( \boxed{120} \) square inches.
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Simplify this solution Beyond the Answer
Great question! If the ratio of the surface area of a cube to the area of one side is 6 to 1, then that means for every unit of area on one side, the total surface area is 6 units. Since Abby measured one side to be 20 square inches, you can simply multiply that by 6. Therefore, the surface area of the entire box is 20 square inches × 6 = 120 square inches! To visualize this, think of a cube – all six sides contribute to a complete outer layer, and given the area of one face, you quickly scale up to find the whole. It's akin to realizing that if one slice of pizza is delicious, the entire pie must be mouthwatering too!
