Answer:
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Explanation:
We can use the given formula to solve for the length of the side of the square-base container:
Volume = side^2 x height
where side is the length of the side of the square base, and height is the height of the container.
We are given that the volume of the container is 3,456 cm³. However, we do not know the height of the container.
To find the length of the side of the square base, we need to first determine the height of the container. We can do this by rearranging the formula:
height = Volume / (side^2)
Plugging in the values we know:
height = 3456 cm³ / (side^2)
We know that the container has a square base, so the length of each side of the base is the same. Therefore, we can write:
Volume = side^2 x side x height
Substituting the expression we found for height:
Volume = side^2 x side x (3456 cm³ / side^2)
Simplifying:
Volume = 3456 cm³ = side^3
Taking the cube root of both sides:
side = ∛3456 cm = 18 cm
Therefore, the length of the side of the square-base container is 18 cm.