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 1,200 square inches than a cube with the surface area of 768 square inches?
$sqrt{2}$ in.
$2sqrt{2}$ in.
$4sqrt{2}$ in.
$36sqrt{2}$ in.

Explanation:

1. First, find the side - length of the cube with surface area \(SA_1 = 1200\) square inches:

• Use the formula \(s=\sqrt{\frac{SA}{6}}\). Substitute \(SA = 1200\) into the formula:
• \(s_1=\sqrt{\frac{1200}{6}}=\sqrt{200}=10\sqrt{2}\) inches.

1. Then, find the side - length of the cube with surface area \(SA_2 = 768\) square inches:

• Substitute \(SA = 768\) into the formula \(s=\sqrt{\frac{SA}{6}}\).
• \(s_2=\sqrt{\frac{768}{6}}=\sqrt{128}=8\sqrt{2}\) inches.

1. Now, find the difference between the two side - lengths:

• \(s_1−s_2 = 10\sqrt{2}-8\sqrt{2}=2\sqrt{2}\) inches.

Answer:

B. \(2\sqrt{2}\) in.