Integrated Math 3 / Unit 7: Geometric Modeling
7.5 Density
Notes
Density $\displaystyle = \frac{\text{mass}}{\text{volume}}$ (or $\displaystyle \frac{\text{amount}}{\text{area}}$ for population density).
- Mass $=$ density $\times$ volume.
- Keep units consistent: g/cm$^3$ goes with cm$^3$.
- An object sinks in water if its density is greater than $1 \text{ g/cm}^3$.
- Example: a block of aluminum 10 cm by 5 cm by 2 cm has volume $100 \text{ cm}^3$. With density $2.7 \text{ g/cm}^3$ its mass is $270$ g.
Practice
An aluminum block is 10 cm by 5 cm by 2 cm. Aluminum has density $2.7 \text{ g/cm}^3$. What is the block's mass?
$V = 100 \text{ cm}^3$ and mass $= 2.7 \cdot 100 = 270$ g.
An object has a mass of 360 g and a volume of $45 \text{ cm}^3$. What is its density, and does it float in water (density $1 \text{ g/cm}^3$)?
$\displaystyle \frac{360}{45} = 8$. That is greater than 1, so it sinks.
A town has 12,000 people living in 4 square miles. What is its population density?
$\displaystyle \frac{12000}{4} = 3000$ people per square mile.
Ready for more? Take the Unit 7 test.