To find the volume of a cube when its surface area is given, we first need to understand the relationship between the surface area and the side length of the cube.
The formula for the surface area (SA) of a cube is:
SA = 6s²
where s is the length of one side of the cube. Given that the surface area is 2400 cm², we can set up the equation:
6s² = 2400
To solve for s², we divide both sides by 6:
s² = 2400 / 6
s² = 400
Now, to find s, we take the square root of 400:
s = √400
s = 20 cm
With the side length s known, we can now find the volume (V) of the cube using the volume formula:
V = s³
V = 20³
V = 8000 cm³
Thus, the volume of the cube is 8000 cm³.