anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
baru
  • baru
\(density=\frac{mass}{volume}\)
anonymous
  • 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
  • anonymous
Oh wait \[3.51 = \frac{ x }{ 712.04 }\] ?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

baru
  • 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
  • anonymous
So would it be: \[3.15 = \frac{ 712.04 }{ x }\] But how would you solve that..?
anonymous
  • anonymous
*oops 3.51
baru
  • baru
you used 'x' to represent volume. so you have been thought some basic algebra?
anonymous
  • anonymous
Yes. Algebra 1, this is Geometry though.. Lol.
baru
  • baru
you have to multiply both sides of the equation by 'x'
anonymous
  • 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
  • baru
\[x \times 3.15 = \frac{x\times 712.04}{x}\]
anonymous
  • anonymous
Yes but if you have a 'x', doesn't it just equal to 1? So '1x' ?
baru
  • baru
i didnt understand what you mean. according to you, what does 'x' represent?
anonymous
  • anonymous
Well, doesn't 1 represents x?
baru
  • baru
No
anonymous
  • anonymous
So how would you find the 'x' in this problem then?
baru
  • 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
  • baru
u understand that?
anonymous
  • anonymous
Yes, I understand that. But isn't the volume going to be one of the answer choices? ^
baru
  • 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
  • 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
  • baru
yes that's definitely one way to do it :)
baru
  • baru
have you learnt how to solve algebraic equations?
UnkleRhaukus
  • 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
  • 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
  • UnkleRhaukus
don't put the numbers in till the equation is solved
anonymous
  • anonymous
So you would divide everything by 3.51?
UnkleRhaukus
  • 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
  • anonymous
So, \[x = \frac{ 712.04 }{ 3.51 } ?\]
UnkleRhaukus
  • UnkleRhaukus
yeahs (but don't forget the units )
anonymous
  • anonymous
So would you start it of by multiplying or dividing? Or is that not the next step.. ?
UnkleRhaukus
  • UnkleRhaukus
compute (712.04 g) รท (3.51 g/cc)
anonymous
  • anonymous
Okay let me do that, give me a minute :). Thanks for helping me
anonymous
  • anonymous
I got 202.86 making sure its g and g/cc
UnkleRhaukus
  • UnkleRhaukus
the units g / (g/cc) = 1/(1/cc) = cc = cubic centimetres
UnkleRhaukus
  • UnkleRhaukus
the grams cancel away
anonymous
  • anonymous
So, would it be the 202? @UnkleRhaukus
UnkleRhaukus
  • UnkleRhaukus
if you round to the nearest hundredth, you answer won't match the options
anonymous
  • anonymous
So you would round that 202.8? @UnkleRhaukus
UnkleRhaukus
  • UnkleRhaukus
i would have had 202.86 cm^3,
anonymous
  • anonymous
So since it's cm^3 would you multiply the 202.86^3? I think that's wrong..
UnkleRhaukus
  • UnkleRhaukus
(the ^3 is only on the unit)
UnkleRhaukus
  • 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
  • anonymous
This is confusing, what would be your next step then to solving the equation?
UnkleRhaukus
  • 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
  • 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
  • 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
  • anonymous
Okay thank you for helping me solve the problem! Sorry it took so long for me to figure out :)
anonymous
  • anonymous
We were right by the way :) The answer was correct. @UnkleRhaukus
UnkleRhaukus
  • UnkleRhaukus
do i get to keep the diamond?
anonymous
  • anonymous
Aha, sure :P. @UnkleRhaukus

Looking for something else?

Not the answer you are looking for? Search for more explanations.