Answer:
The length of a side of the cube-shaped container is 2,016 units
Step-by-step explanation:
step 1
Find the volume of a cube with a side length of 1008 units
The volume of a cube is equal to
![V=b^3](https://tex.z-dn.net/?f=V%3Db%5E3)
where
b is the length side of the cube
we have
![b=1,008\ units](https://tex.z-dn.net/?f=b%3D1%2C008%5C%20units)
substitute
![V=(1,008)^3\ units^3](https://tex.z-dn.net/?f=V%3D%281%2C008%29%5E3%5C%20units%5E3)
step 2
Find the length side of the cube-shaped container
Let
x-----> the length side of the cube-shaped container in units
we know that
The area of the base of the cube-shaped container multiplied by 252 units must be equal to the volume of the cube with a side length of 1008 units
so
![x^{2} (252)=(1,008)^3](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%28252%29%3D%281%2C008%29%5E3)
solve for x
![x^{2} =\frac{(1,008)^3}{252}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D%5Cfrac%7B%281%2C008%29%5E3%7D%7B252%7D)
![x^2=4,064,256](https://tex.z-dn.net/?f=x%5E2%3D4%2C064%2C256)
![x=\sqrt{4,064,256}](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B4%2C064%2C256%7D)
![x=2,016\ units](https://tex.z-dn.net/?f=x%3D2%2C016%5C%20units)
therefore
The length of a side of the cube-shaped container is 2,016 units