Question

A cube with a side length of 1008 units is dropped and completely submerged in a cube-shaped container. If the water level in the cube-shaped container rises 252 units. Find the length of a side of the cube-shaped container.

Answer 1

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

$V=b^3$

where

b is the length side of the cube

we have

$b=1,008\ units$

substitute

$V=(1,008)^3\ units^3$

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

$x^{2} (252)=(1,008)^3$

solve for x

$x^{2} =\frac{(1,008)^3}{252}$

$x^2=4,064,256$

$x=\sqrt{4,064,256}$

$x=2,016\ units$

therefore

The length of a side of the cube-shaped container is 2,016 units