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?

1 Answer
Jun 21, 2018

#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#