1 litre of paint covers an area of 12m^2 . Work out the thickness, in cm, of the coat of paint.

[bumblebee123]

I've been puzzling over this question for a long time and I still can't think where to start. It sounds so simple, but I've never come across a question like this before. Can anyone help to explain?

the question is: 1 litre of paint covers an area of 12m^2 . Work out the thickness, in cm, of the coat of paint. Give your answer in standard form.

Thanks for any help

 

[Harry_the_cat]

It will help if you know that 1 litre of paint has a volume of 1000 cubic cm.

 

[bumblebee123]

I know 1000cm^3 = 1 litre

They want to know depth so,
length x width x depth

I am given area so,

12m^2 x depth = 1000cm^3

divide 1000 by 12 ..... which is not right, where am I going wrong?

 

[Dr.Peterson]

I know 1000cm^3 = 1 litre

They want to know depth so,
length x width x depth

I am given area so,

12m^2 x depth = 1000cm^3

divide 1000 by 12 ..... which is not right, where am I going wrong?

Units matter!

Dividing 1000 cm^3 by 12 m^2 doesn't give an answer in cm; it will be in cm^3/m^2.

First convert m^2 to cm^2 (careful!). Then you can divide.

 

[bumblebee123]

Thank you. I forgot. So now I have 12m^2 x 100 = 1200cm^2
This gives me 1000cm^3/1200cm^2
but it's still not the right answer as it should be 7.67 x 10^4

 

[Dr.Peterson]

Thank you. I forgot. So now I have 12m^2 x 100 = 1200cm^2
This gives me 1000cm^3/1200cm^2
but it's still not the right answer as it should be 7.67 x 10^4

Really? A coat of paint 76,700 cm thick?? Maybe you looked at the wrong answer.

Remember I added "(careful!)"? There was a reason for that! To convert m to cm, you multiply by 100; but to convert m^2 to cm^2, you have to multiply by 100^2 = 10000. (One square meter is 100 cm on a side, so its area is 100*100 cm^2.)

So the correct answer is 1000 cm^3 / 120000 cm^2 = 0.00833 cm.

 

[MarkFL]

You want:

[MATH]V=Ah[/MATH]
[MATH]1000\text{ cm}^3=\left(12\text{ m}^2\left(\frac{100\text{ cm}}{1\text{ m}}\right)^2\right)h[/MATH]
[MATH]h=\frac{1000}{120000}\,\text{cm}=\frac{1}{120}\,\text{cm}=8.\overline{3}\times10^{-3}\text{ cm}[/MATH]

 

[bumblebee123]

Really? A coat of paint 76,700 cm thick?? Maybe you looked at the wrong answer.

Remember I added "(careful!)"? There was a reason for that! To convert m to cm, you multiply by 100; but to convert m^2 to cm^2, you have to multiply by 100^2 = 10000. (One square meter is 100 cm on a side, so its area is 100*100 cm^2.)

So the correct answer is 1000 cm^3 / 120000 cm^2 = 0.00833 cm.

sorry, you were right- I read the wrong answer! It's 8.3 x 10^-3

that makes a lot more sense, thanks

 

[Harry_the_cat]

Thank you. I forgot. So now I have 12m^2 x 100 = 1200cm^2
This gives me 1000cm^3/1200cm^2
but it's still not the right answer as it should be 7.67 x 10^4

You made a very common error here.

Remember:
100 cm = 1 metre
(100^2) cm^2 = 1 metre^2
(100^3) cm^3 = 1 metre^3

That applies to all similar conversions.