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? $\sqrt{35}$ m, $\sqrt{210}$ m, $7\sqrt{5}$ m, $\sqrt{5}$ m

Explanation:

Step1: Find side for SA=480

Use formula \( s = \sqrt{\frac{SA}{6}} \). Substitute \( SA = 480 \):
\( s_1 = \sqrt{\frac{480}{6}} = \sqrt{80} = 4\sqrt{5} \).

Step2: Find side for SA=270

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

Step3: Calculate the difference

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

Answer:

\(\boldsymbol{\sqrt{5}\ \text{m}}\) (the option with \(\sqrt{5}\ \text{m}\))