A large diamond with a mass of 712.04 grams was recently discovered in a mine. If the density of the diamond is 3.51 grams over centimeters cubed, what is the volume? Round your answer to the nearest hundredth.
202.9 cm3
507.02 cm3
717.06 cm3
3574.44 cm3

- anonymous

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- baru

\(density=\frac{mass}{volume}\)

- anonymous

So would you do this: \[density = \frac{ x}{ 712.04 }\] ? I don't understand if it says that denisty is already found (3.51)...?

- anonymous

Oh wait \[3.51 = \frac{ x }{ 712.04 }\] ?

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## More answers

- baru

the idea you have is correct,
but you have mixed up mass and volume.
x should be in the denominator and 712.04 in the numerator

- anonymous

So would it be: \[3.15 = \frac{ 712.04 }{ x }\] But how would you solve that..?

- anonymous

*oops 3.51

- baru

you used 'x' to represent volume. so you have been thought some basic algebra?

- anonymous

Yes. Algebra 1, this is Geometry though.. Lol.

- baru

you have to multiply both sides of the equation by 'x'

- anonymous

So you'd multiply 'x' by 712.04? Wouldn't you get the same answer (712.04) I'm a little lost.. Or would you multiply the 3.51 to 712.04?

- baru

\[x \times 3.15 = \frac{x\times 712.04}{x}\]

- anonymous

Yes but if you have a 'x', doesn't it just equal to 1? So '1x' ?

- baru

i didnt understand what you mean.
according to you, what does 'x' represent?

- anonymous

Well, doesn't 1 represents x?

- baru

No

- anonymous

So how would you find the 'x' in this problem then?

- baru

\(density=\frac{mass}{volume}\)
we know density, we know mass...
but we do not know volume . so we have used the letter 'x' like a shortform for 'volume' and substituted into the above formula.
so 'x' represents 'volume'
and volume is the quantity that the question is asking us to find

- baru

u understand that?

- anonymous

Yes, I understand that. But isn't the volume going to be one of the answer choices? ^

- baru

all the options given are possible values for 'volume' but only one of them is correct.
we have to find which one by using our equation

- anonymous

So, I'm guessing you would take each 'volume' and replace it for 'x' to see which one is right in the equation?

- baru

yes that's definitely one way to do it :)

- baru

have you learnt how to solve algebraic equations?

- UnkleRhaukus

density = mass / volume
we can rearrange the equation by multiplying both side by the volume and,
density * volume = (mass / volume) * volume
= mass
dividing both side by the density
density * volume / density = mass / density
we get
volume = mass / density

- anonymous

Well yeah, but I'm kinda forgetful.. I know how to solve most but this one is giving me problems xD. So would the next step be this: \[202.9 \times 3.51 = \frac{ 202.9 \times 712.04 }{ x }\] ?

- UnkleRhaukus

don't put the numbers in till the equation is solved

- anonymous

So you would divide everything by 3.51?

- UnkleRhaukus

We start the definition of density
density = mass / volume
we rearrange the equation so solve to volume (as the question asks for)
volume = mass / density
now we use the values
mass = 712.04 g
density = 3.51 g/cc
plug these values into the equation

- anonymous

So, \[x = \frac{ 712.04 }{ 3.51 } ?\]

- UnkleRhaukus

yeahs (but don't forget the units )

- anonymous

So would you start it of by multiplying or dividing? Or is that not the next step.. ?

- UnkleRhaukus

compute (712.04 g) รท (3.51 g/cc)

- anonymous

Okay let me do that, give me a minute :). Thanks for helping me

- anonymous

I got 202.86 making sure its g and g/cc

- UnkleRhaukus

the units g / (g/cc) = 1/(1/cc) = cc = cubic centimetres

- UnkleRhaukus

the grams cancel away

- anonymous

So, would it be the 202? @UnkleRhaukus

- UnkleRhaukus

if you round to the nearest hundredth, you answer won't match the options

- anonymous

So you would round that 202.8? @UnkleRhaukus

- UnkleRhaukus

i would have had 202.86 cm^3,

- anonymous

So since it's cm^3 would you multiply the 202.86^3? I think that's wrong..

- UnkleRhaukus

(the ^3 is only on the unit)

- UnkleRhaukus

one could argue that the last two digits are invalid, as 3.51 has only three significant figures of accuracy ,
so that 203 cm^3, is more true

- anonymous

This is confusing, what would be your next step then to solving the equation?

- UnkleRhaukus

it's multiple choice right, one of the answers is correct,
we followed the right steps and got an answer that was almost exactly a match,
(all the other options are way off)

- anonymous

So I was right about the 202.8? We just had to round it up, and it should be close to the first option?

- UnkleRhaukus

You were right with 202.86 cm3
Best match is A 202.9 cm3
(we have to ignore the rounding error i guess )

- anonymous

Okay thank you for helping me solve the problem! Sorry it took so long for me to figure out :)

- anonymous

We were right by the way :) The answer was correct. @UnkleRhaukus

- UnkleRhaukus

do i get to keep the diamond?

- anonymous

Aha, sure :P. @UnkleRhaukus

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