What is the volume of a cube if its surface area is 2400 cm²?

The surface area of a cube is calculated using the formula:

Surface Area = 6 × a²

Where a represents the length of one side of the cube. If we know the surface area is 2400 cm², we can set up the equation:

2400 = 6 × a²

To find the length of a, we first divide both sides by 6:

a² = 2400 / 6

Calculating the right-hand side gives us:

a² = 400

Now, we take the square root of both sides to find a:

a = √400

This simplifies to:

a = 20 cm

Now that we have the length of one side of the cube, we can calculate the volume. The volume of a cube is calculated using the formula:

Volume = a³

Substituting the value we’ve found for a:

Volume = 20³

Calculating this gives:

Volume = 8000 cm³

So, the volume of the cube is 8000 cm³.