Question

Question #2a36d

Answer 1

approximately `98.53color(white)(i)cm^3`

Explanation:

Step 1
Imagine a cube box.

Based on this image, we can see that there are `6` sides.

To find the maximum possible volume for the box, we must determine two things - the area of one side and the side length. Knowing that there is `128color(white)(i)cm^2` of material, we can divide `128color(white)(i)cm^2` by `6` to give us the area for one side of the box.

`128color(white)(i)cm^2-:6`
`=64/3color(white)(i)cm^2`

Step 2
We can now use the calculated value to determine the side length of the box. Recall that the area of a square is given by:

`color(blue)(|bar(ul(color(white)(a/a)A=s^2color(white)(a/a)|)))`

`ul("where:")`
`A=`area
`s=`side length

Now that we have determined a relationship between area and side length, we can plug our values into the formula to determine the side length.

`A=s^2`

`s=+-sqrt(A)`

`s=+-sqrt(64/3)`

Note: Since a measurement cannot be negative, the only valid answer is `8/sqrt(3)` and not `-8/sqrt(3)` !

`s=8/sqrt(3)`

Step 3
Since we have now determined the side length, we can use the formula for volume of a cube to determine its maximum possible volume:

`color(blue)(|bar(ul(color(white)(a/a)V=s^3color(white)(a/a)|)))`

`ul("where:")`
`V=`volume
`s=`side length

Plugging in the values,

`V=s^3`

`V=(8/sqrt(3))^3`

`V=512/(3sqrt(3))`

`V~~color(green)(|bar(ul(color(white)(a/a)color(black)(98.53color(white)(i)cm^3)color(white)(a/a)|)))`