Question

The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot 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?

Answer 1

Its B

Explanation:

Edge 2021

Answer 2

`2√(2)\ ft\ longer`

Explanation:

Area Of A Cube

Suppose a cube with side length s, the area of one side is

`A_s=s^2`

Since the cube has 6 sides, the total area is

`A=6A_s=6s^2`

But if we have the area, we can solve the above formula for s to get

`A=6s^2`

`\displaystyle s=\sqrt{(A)/(6)}`

We have two different cubes with areas 1,200 square inches and 768 square inches. Let's compute their side lengths

`\displaystyle s_1=\sqrt{(1,200)/(6)}=√(200)`

`\displaystyle s_1=10√(2)\ ft`

`\displaystyle s_2=\sqrt{(768)/(6)}=√(128)`

`\displaystyle s_2=8√(2) ft`

The difference between them is

`10√(2)\ ft-8√(2)\ ft=2√(2)\ ft\approx 2.83\ ft`

The side of the cube with area 1,200 square inches is
`2√(2)\ ft` longer then the side of the cube with area 768 square inches