Dimensional Analysis
Answer:
- [tex]320\text{cm}^3[/tex] is [tex]\bold{0.00032\text{m}^3}[/tex] if written in [tex]\text{m}^3[/tex]
- [tex]320\text{cm}^3[/tex] is [tex]\bold{320000\text{mm}^3}[/tex] if written in [tex]\text{mm}^3[/tex]
Step-by-step explanation:
Rewriting [tex]320cm^3[/tex] in [tex]m^3[/tex]:
[tex]320\text{c\text{m}}^3 \\ 320\text{c\text{m}}^3 \cdot \frac{\text{m}}{100\text{c\text{m}}} \\320\text{c\text{m}}^3 \cdot (\frac{\text{m}}{100\text{c\text{m}}})^3 \\ 320\text{c\text{m}}^3 \cdot \frac{\text{m}^3}{100^3 \cdot \text{c\text{m}}^3} \\ 320\text{c\text{m}}^3 \cdot \frac{\text{m}^3}{1000000\text{c\text{m}}^3} \\ \frac{320\text{c\text{m}}^3 \cdot \text{m}^3}{1000000\text{c\text{m}}^3} \\ \frac{32\text{m}^3}{100000} \\ \frac{32}{100000}\text{m}^3 \\ 0.00032\text{m}^3[/tex]
Rewriting [tex]320cm^3[/tex] in [tex]mm^3[/tex]:
[tex]320\text{cm}^3[/tex] in [tex]\text{mm}^3[/tex]:
[tex]320\text{cm}^3 \\ 320\text{cm}^3 \cdot \frac{\text{mm}}{0.1\text{cm}} \\ 320\text{cm}^3 \cdot (\frac{\text{mm}}{0.1\text{cm}})^3 \\ 320\text{cm}^3 \cdot \frac{\text{mm}^3}{0.1^3 \cdot \text{cm}^3} \\ 320\text{cm}^3 \cdot \frac{\text{mm}^3}{0.001\text{cm}^3} \\ \frac{320\text{cm}^3 \cdot \text{mm}^3}{0.001\text{cm}^3} \\ \frac{320\text{mm}^3}{0.001} \\ 320000\text{mm}^3[/tex]
