Question

the formula S=√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 coube with a surface area of 180 square meters than a cube with the surface area of 120 square meters?

Answer 1

Using the formula S=√SA/6, we can find the length of the side of a cube with a given surface area.

For a cube with a surface area of 120 square meters, we have:

S = √(120)/6 = √20 ≈ 4.47 meters

For a cube with a surface area of 180 square meters, we have:

S = √(180)/6 = √30 ≈ 5.48 meters

Therefore, the difference in the length of the sides of the two cubes is:

5.48 - 4.47 = 1.01 meters

So the side of the cube with a surface area of 180 square meters is 1.01 meters longer than the side of the cube with a surface area of 120 square meters.

Answer 2

1.01 m

Explanation:

The following formula gives the side length (s) of a cube with a surface area (SA):

`s=\sqrt{(SA)/(6)}`

If a cube has a surface area of 180 m², then its side length is:

`s=\sqrt{(180)/(6)}`

`s=√(30)\; \sf m`

If a cube has a surface area of 120 m², then its side length is:

`s=\sqrt{(120)/(6)}`

`s=√(20)`

`s=√(4 \cdot 5)`

`s=√(4) √(5)`

`s=2√(5)\; \sf m`

To calculate how much longer the side of a cube with a surface area of 180 m² is than a cube with the surface area of 120 m², subtract the side lengths:

`\begin{aligned}√(30)-2√(5)&=1.0050896...\\\\&= 1.01\; \sf m\; (nearest\;hundredth)\end{aligned}`

Therefore, the side of the cube with a surface area of 180 m² is 1.01 m longer than the side of the cube with a surface area of 120 m².