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
[tex]V=b^3[/tex]
where
b is the length side of the cube
we have
[tex]b=1,008\ units[/tex]
substitute
[tex]V=(1,008)^3\ units^3[/tex]
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
[tex]x^{2} (252)=(1,008)^3[/tex]
solve for x
[tex]x^{2} =\frac{(1,008)^3}{252}[/tex]
[tex]x^2=4,064,256[/tex]
[tex]x=\sqrt{4,064,256}[/tex]
[tex]x=2,016\ units[/tex]
therefore
The length of a side of the cube-shaped container is 2,016 units
