Question

PLEASEE HELP ANYONE GOOD AT MATH!!!

Answer 1

In order for you to solve this question, you need you plug in the surface area in the equation for you to obtain the side lengths and compare them to get the difference.

Let's start with the one with a surface area of 480.
s= sqrt(480/6)
s = sqrt (80)

Then the one with a surface area of 270.
s = sqrt(270/6)
s = sqrt (45)

Now that you've found both side lengths, you find the difference by subtracting sqrt80 and sqrt45. The difference would be the square root of 5.

Answer 2

$\bf \textit{side of a cube with SA of 480}\implies s=\sqrt{\cfrac{480}{6}}\implies s=\sqrt{80} \\\\\\ \textit{side of a cube with SA of 270}\implies s=\sqrt{\cfrac{270}{6}}\implies s=\sqrt{45}\\\\ -------------------------------$

$\bf \cfrac{\textit{larger side}}{\textit{smaller side}}\qquad \cfrac{\sqrt{80}}{\sqrt{45}}\quad \begin{cases} 80=2\cdot 2\cdot 2\cdot 2\cdot 5\\ \qquad 4^2\cdot 5\\ 45=3\cdot 3\cdot 5\\ \qquad 3^2\cdot 5 \end{cases}\implies \cfrac{\sqrt{4^2\cdot 5}}{\sqrt{3^2\cdot 5}} \\\\\\ \cfrac{\textit{larger side}}{\textit{smaller side}}\qquad\cfrac{4\sqrt{5}}{3\sqrt{5}}\implies \cfrac{4}{3}\impliedby \textit{larger side is }\frac{1}{3}\textit{ larger}$