the formula $s = sqrt{\frac{sa}{6}}$ gives the length of the side, s, of a cube with a surface area, sa. how…

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?\n$sqrt{30}-4sqrt{5}\text{ m}$\n$sqrt{30}-2sqrt{5}\text{ m}$\n$sqrt{10}\text{ m}$\n$2sqrt{15}\text{ m}$

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?\n$sqrt{30}-4sqrt{5}\text{ m}$\n$sqrt{30}-2sqrt{5}\text{ m}$\n$sqrt{10}\text{ m}$\n$2sqrt{15}\text{ m}$

Answer

Explanation:

Step1: Find side length for SA = 180

Substitute SA = 180 into $s=\sqrt{\frac{SA}{6}}$. $s_1=\sqrt{\frac{180}{6}}=\sqrt{30}$

Step2: Find side length for SA = 120

Substitute SA = 120 into $s=\sqrt{\frac{SA}{6}}$. $s_2=\sqrt{\frac{120}{6}}=\sqrt{20}=2\sqrt{5}$

Step3: Find the difference

Calculate $s_1 - s_2$. $s_1 - s_2=\sqrt{30}-2\sqrt{5}$

Answer:

$\sqrt{30}-2\sqrt{5}\text{ m}$