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 180 square meters than a cube with the surface area of 120 square meters?
\\( \sqrt{30} - 4\sqrt{5} \\) m
\\( \sqrt{30} - 2\sqrt{5} \\) m
\\( \sqrt{10} \\) m
\\( 2\sqrt{15} \\) m

Explanation:

Step1: Find side for SA=180

Using \( s = \sqrt{\frac{SA}{6}} \), substitute \( SA = 180 \):
\( s_1 = \sqrt{\frac{180}{6}} = \sqrt{30} \)

Step2: Find side for SA=120

Substitute \( SA = 120 \) into the formula:
\( s_2 = \sqrt{\frac{120}{6}} = \sqrt{20} = 2\sqrt{5} \)

Step3: Find the difference

Subtract \( s_2 \) from \( s_1 \):
\( s_1 - s_2 = \sqrt{30} - 2\sqrt{5} \)

Answer:

\(\boldsymbol{\sqrt{30} - 2\sqrt{5}}\) m (corresponding to the option \(\sqrt{30} - 2\sqrt{5}\) m)