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

Question

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

baru · Answer

$density=\frac{mass}{volume}$

anonymous · Answer

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 · Answer

Oh wait $$3.51 = \frac{ x }{ 712.04 }$$ ?

baru · Answer

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 · Answer

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

anonymous · Answer

*oops 3.51

baru · Answer

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

anonymous · Answer

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

baru · Answer

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

anonymous · Answer

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 · Answer

$$x \times 3.15 = \frac{x\times 712.04}{x}$$

anonymous · Answer

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

baru · Answer

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

anonymous · Answer

Well, doesn't 1 represents x?

baru · Answer

No

anonymous · Answer

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

baru · Answer

$density=\frac{mass}{volume}$

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 · Answer

u understand that?

anonymous · Answer

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

baru · Answer

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 · Answer

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

baru · Answer

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

baru · Answer

have you learnt how to solve algebraic equations?

unklerhaukus · Answer

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 · Answer

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 · Answer

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

anonymous · Answer

So you would divide everything by 3.51?

unklerhaukus · Answer

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 · Answer

So, $$x = \frac{ 712.04 }{ 3.51 } ?$$

unklerhaukus · Answer

yeahs (but don't forget the units )

anonymous · Answer

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

unklerhaukus · Answer

compute    (712.04 g) ÷ (3.51 g/cc)

anonymous · Answer

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

anonymous · Answer

I got 202.86 making sure its g and g/cc

unklerhaukus · Answer

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

unklerhaukus · Answer

the grams cancel away

anonymous · Answer

So, would it be the 202? @UnkleRhaukus

unklerhaukus · Answer

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

anonymous · Answer

So you would round that 202.8?  @UnkleRhaukus

unklerhaukus · Answer

i would have had    202.86 cm^3,

anonymous · Answer

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

unklerhaukus · Answer

(the  ^3  is only on the unit)

unklerhaukus · Answer

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 · Answer

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

unklerhaukus · Answer

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 · Answer

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 · Answer

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

anonymous · Answer

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

anonymous · Answer

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

unklerhaukus · Answer

do i get to keep the diamond?

anonymous · Answer

Aha, sure :P. @UnkleRhaukus