Metric Conversions

Please can someone help me with question 19? I've imagined the rug being a cuboid but then imagined it being flat with 2 sides. My working out is probably wrong too because of this. I dont know how to link the surface area of the top side of the rug with the overall weight of it.

Can you explain why you multiplied 6175 by 2?

I dont think i shouldve. It just confused me that it only gave me the top surface area so i multiplied it by 2 to get the top and bottom. Is the rest of my method correct provided i didnt multiply by 2 at the beginning?

Multiplying it by 2 makes me think that you don't fully understand the question. Make sure you think hard about what's going on and realise why you only need to care about the area of the top of the rug since the question asks for the weight of a 1cm x 1cm section.

It looks like you've converted inches² to cm² by multiplying by 2.54. But that's not how you convert square units. Do you know how to correct it?

I would have done this question by changing all the units into metric before doing anything else e.g. 65 inches = __ cm, 95 inches = ___ cm etc.

Multiplying it by 2 makes me think that you don't fully understand the question. Make sure you think hard about what's going on and realise why you only need to care about the area of the top of the rug since the question asks for the weight of a 1cm x 1cm section.

It looks like you've converted inches² to cm² by multiplying by 2.54. But that's not how you convert square units. Do you know how to correct it?

I would have done this question by changing all the units into metric before doing anything else e.g. 65 inches = __ cm, 95 inches = ___ cm etc.

Ok is my final answer 0.347g?

Yes that's correct.

Yes that's correct.

Please can you help me with question 22?
I know the equation for density but I don’t know if that will help.

From the information you can work out the volume of metal A and the volume of metal B in the alloy. Then think about how you can use this to find the total density of the alloy.

This is a very common density question that could appear in the exam.

$mass\div density = volume$
Therefore I do 250÷8.9 to work out the volume of metal A and 250÷2.7 to work out the volume of metal B? Or is it ÷8.9³ and ÷2.7³? Or am I totally wrong?

No that's right. You don't need to cube the densities because the formula is

density = mass/volume

so volume = mass / density

You're given the density in g/cm³ and the weight is in grams so the units match up and dividing will give you the volume in cm³.

You can also see this by dividing the units algebraically:

$g \div \frac{g}{cm^3} = g \times \frac{cm^3}{g} = cm^3$

Do you know what to do next?

Yes I understand this bit now. So ive done both calculations then added them together to get the total volume of the alloy which is 120.6824802cm^3. Then I need to work out the density so I do 500/120.68...... to get the density of the alloy as 4.1g/cm^3. Is this correct?

That's right. I bet that a lot of people for this question would just find the mean of the densities since the masses are the same because this seems intuitive.

But if you do that you get (8.9+2.7)/2 = 5.8 which is incorrect.

This method would only work if mass and density were directly proportional but they're actually inversely proportional.

That's right.

Yep! This is doing the same... weird. And the thread title is standard.


@Amusing Elk