Question

Convert 320cm^3 to m^3 and mm^3​

Answer 1

Dimensional Analysis

Answer:

• 
  `320\text{cm}^3` is
  `\bold{0.00032\text{m}^3}` if written in
  `\text{m}^3`
• 
  `320\text{cm}^3` is
  `\bold{320000\text{mm}^3}` if written in
  `\text{mm}^3`

Explanation:

Rewriting
`320cm^3` in
`m^3`:

`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} \\ (32)/(100000)\text{m}^3 \\ 0.00032\text{m}^3`

Rewriting
`320cm^3` in
`mm^3`:

`320\text{cm}^3` in
`\text{mm}^3`:

`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`