# science question, but its also kinda math?

#### jazzywazzers

##### New member
The density of gold is 19.3 g/cm 3, What is the mass of 15cm 3 of gold?

I just cant seem to figure this one out, thank you in advance!

#### MarkFL

##### Super Moderator
Staff member
Hello, and welcome to FMH!

This statement:

"The density of gold is 19.3 g/cm^3"

tells is that for each cubic centimeter of gold, we will have 19.3 grams. So, what do you think we need to do in order to determine the mass of 15 cubic centimeters of gold?

#### jazzywazzers

##### New member
Hello, and welcome to FMH!

This statement:

"The density of gold is 19.3 g/cm^3"

tells is that for each cubic centimeter of gold, we will have 19.3 grams. So, what do you think we need to do in order to determine the mass of 15 cubic centimeters of gold?
if it was the mass of gold then I'd simply multiply by 15 but since its the density I'm not sure what next step to take

#### MarkFL

##### Super Moderator
Staff member
Yes, you want to multiply. Mass density $$\rho$$ is defined as mass $$m$$ per volume $$V$$:

$$\displaystyle \rho\equiv\frac{m}{V}$$

And this implies (by algebraically rearranging by multiplying both sides by $$V$$):

$$\displaystyle m=\rho V$$

This tells us that we can determine the mass if we know the mass density and the volume by computing the product of these two quantities. Hence:

$$\displaystyle m=\left(19.3\frac{\text{g}}{\text{cm}^3}\right)\left(15\text{ cm}^3\right)=\,?$$

#### mmm4444bot

##### Super Moderator
Staff member
This conversion method goes by different names, but in chemistry it's usually called "dimensional analysis".

To find lessons/videos (with examples) on this topic, google keywords: chemistry "dimensional analysis" "conversion factors". Chemistry classes use these types of conversion ratios a lot.

For example, to find the grams of a particular substance produced from a chemical reaction, where you know the grams of a related substance that went into the reaction, you might need to (1) convert known grams of the related molecule to moles, (2) convert moles of that molecule to moles of the molecule of interest and then (3) convert the moles of that substance into grams.

Cheers