Question

Allie used 14.0m3 of cement to make a square patio. if the thickness of the patio is 20 cm, the length of the patio must be?

allie used 14.0m3 of cement to make a square patio. if the thickness of the patio is 20 cm, the length of the patio must be?

Answer 1

`color(blue)(sqrt(70)" m")`

Explanation:

There are different ways of doing this, and this is just one way.

`20cm=0.2m`

If we consider a piece of concrete that is `1mxx1mxx0.2m`

Now we find the volume of this:

`1xx1xx0.2=0.2m^3`

We then divide `14m^3` by this. This will tell us how many of these `1mxx1mxx0.2m` pieces we can get from the given volume.

`14/0.2=70`

This means we have `70` square metres of concrete at a thickness of `0.2m`

We need the patio to be square, so if the sides are x metres:

`x^2=70`

`x=sqrt(70)" m"` ( we do not need to be concerned with negative roots here )

So each side is `sqrt(70) " m"` long.

We can check this by finding the volume of the patio.

`sqrt(70)mxxsqrt(70)mxx0.2m=14m^3`