Question

the formula $s = \sqrt{\frac{sa}{6}}$ 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?
\\( \sqrt{5} \\) m
\\( \sqrt{35} \\) m
\\( \sqrt{210} \\) m
\\( 7\sqrt{5} \\) m

Explanation:

Step1: Find side length for SA = 480

Using formula \( s = \sqrt{\frac{SA}{6}} \), substitute \( SA = 480 \):
\( s_1 = \sqrt{\frac{480}{6}} = \sqrt{80} = 4\sqrt{5} \)

Step2: Find side length for SA = 270

Substitute \( SA = 270 \) into the formula:
\( s_2 = \sqrt{\frac{270}{6}} = \sqrt{45} = 3\sqrt{5} \)

Step3: Find the difference

Subtract \( s_2 \) from \( s_1 \):
\( s_1 - s_2 = 4\sqrt{5} - 3\sqrt{5} = \sqrt{5} \)

Answer:

\(\sqrt{5}\) m (corresponding to the first option: \(\boldsymbol{\sqrt{5}}\) m)