The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 480 square meters than a cube with the surface area of 270 square meters? StartRoot 5 EndRoot m StartRoot 35 EndRoot m StartRoot 210 EndRoot m 7 StartRoot 5 EndRoot m

The side of a cube with a surface area of 480 square meters is [tex]\sqrt 5[/tex] meters longer than a cube with the surface area of 270 square meters

What is surface area?

The surface area of a shape is the amount of space on the shape

The formula is given as:

[tex]s = \sqrt{\frac{S}{6}}[/tex]

When the surface area is 480 square meters, we have:

[tex]s_1 = \sqrt{\frac{480}{6}}[/tex]

Evaluate the quotient

[tex]s_1 = \sqrt{80}[/tex]

Simplify

[tex]s_1 = 4\sqrt{5}[/tex]

When the surface area is 270 square meters, we have:

[tex]s_2 = \sqrt{\frac{270}{6}}[/tex]

Evaluate the quotient

[tex]s_2 = \sqrt{45}[/tex]

Simplify

[tex]s_2 = 3\sqrt{5}[/tex]

Calculate the difference (d)

[tex]d =s_1 -s_2[/tex]

So, we have:

[tex]d =4\sqrt 5 - 3\sqrt5[/tex]

Evaluate

[tex]d = \sqrt5[/tex]

Hence, the side of a cube with a surface area of 480 square meters is [tex]\sqrt 5[/tex] meters longer than a cube with the surface area of 270 square meters