Diamonds are measured in carats (1.0 carat=0.200g). The density of diamond is 3.51 g/cm^3. What is the VOLUME of a 5.0 carat diamond?
You're given two things and asked to find another. You're given density, mass, and asked to find the volume.
The formula for density is:
D= Mass
------
Volume
Rewrite this formula for Volume and you get:
V= M
---
D
A 5.0 carat diamond will have a mass of:
5(0.200 g)= 1 g. You are already given the density of 3.51, so all that's left to do is plug in.
V= 1g/3.51 g.cm^3= .285 cm^3
What is measured in carats
a quarter has a mass of 5.63g. what is its mass in kilograms? milligrams?
Well, if a 1.0 carat diamond weighs 0.200 grams, then a 5.0 carat diamond would weigh 1.0 gram. Now, since the density of diamond is 3.51 g/cm^3, you can calculate the volume by dividing the weight by the density.
But hey, I'm no mathematician, I'm just here to make people smile! So let's say the volume of a 5.0 carat diamond is equal to... umm... the volume of a clown's honking nose! Trust me, it's a big volume! But seriously, I think the formula you need is weight/density to calculate the volume of that diamond. Good luck!
To find the volume of a 5.0 carat diamond, we need to determine the mass of the diamond first. Since 1.0 carat is equal to 0.200g, to find the mass of a 5.0 carat diamond, we multiply 5.0 carats by the conversion factor:
5.0 carat * 0.200g = 1.0g
Now that we know the mass of the diamond is 1.0g, we can use the formula for density, which is mass divided by volume:
Density = mass / volume
Rearranging the formula to solve for volume gives us:
Volume = mass / density
Plugging in the values we have:
Volume = 1.0g / 3.51 g/cm^3
Calculating this:
Volume = 0.284 cm^3
Therefore, the volume of the 5.0 carat diamond is 0.284 cm^3.