If you have 2400 cm2 of material available to cover a cube;

Then what is the maximum volume of the cube?

let its side length = x

=> 2400 = 6x^2

=> x^2 = 400 => x = 20 cm

so its volume = 20^3 = 8000 cm^3

Both the surface area and the volume of a cube depends on just one parameter: the length of each side of the cube.

The surface area of the cube is calculated by 6s², where s is the length of a side. The volume is calculated by s³.

Since you have 2400 cm² of material to cover the cube, we match that with the surface area.

2400 cm² = 6s²
s = 20 cm

The volume of the cube is thus s³ = (20 cm)³ = 8000 cc.

A cube has six square faces. So each face would have an area of 2400/6 = 400 cm2

That's a square that is 20 cm by 20 cm

A cube with an edge of 20 cm has a volume of 20^3 or 20x20x20 = 8000 cm3

Surface area of cube = 6(side)² = 2400 cm²

side² = 2400 / 6 = 400
side = √400= 20 cm

Volume of cube = side³ = 20³ = 8000 cm³

Area of a cube = 6x² = 2400
x² = 2400/6 = 400
x = 20

Volume of a cube = x³ = 20³ = 8000 cm³

SA = 6s^2
2400 = 6s^2
400 = s^2
20 = s

V = s^3
V = 20^3
V = 8000

8000 cm^3

8000cc