\(\displaystyle \frac{210\: \text{cm}^{3}}{1} \times \frac{1\:\text {in}^{3}}{16.387\:\text {cm}^{3}} = 12.8\:\text {in}^{3}\)

\( \displaystyle \frac{91,227,778\:\text{ft}^{3}}{1} \times \frac{0.02832\:\text{m}^{3}}{1\:\text {ft}^{3}} = 2,583,283\:\text{m}^{3}\)
(Slight differences in rounding can cause the final answer to be off by a few numbers.)

\(\displaystyle \frac{350\:\text {cm}^{3}}{1} \times \frac{1\:\text {ml}}{1\:\text {cm}^{3}} = 350\:\text {ml}\)

\(\displaystyle \frac{30\:\text {m}^{3}}{1} \times \frac{1\:\text {yd}^{3}}{0.7646\:\text {m}^{3}} = 39.24\text {yd}^{3}\)

Written Solution:

Step 1: Start with what you know.

We need to fill an area with dirt that measures 2 m × 3 m × 5 m. To find the volume, we multiply the three dimensions together: \(2\:\text{m}\times3\:\text{m}\times5\:\text{m}=30\:\text{m}^{3}\)

So we need \(30\:\text{m}^{3}\) of dirt.

Step 2: Determine what you want to get in the end. (Figure out what the end units should be.) = \(\text{yd}^{3}\)

Step 3: Determine what conversion factor(s) to use. You may sometimes need more than one.



We know that 1 yd = 0.9144 m and we can use this information to find \( \text {yd}^3\):

1 yd = 0.9144 m

Cube both sides of the equation:

\(\text{(1 yard)}^{3}\) = \(\text{(0.9144 m)}^{3}\)

Step 4: Multiply by 1 in the form of the conversion factor that cancels out the unwanted units.

We have \( 30 \text {m}^3 \) so we need to multiply it by \( \dfrac{1\:\text{yd}^{3}}{0.7646\:\text{m}^{3}}\)

Note that we chose the conversion factor that will enable us to cancel out the existing units and change them to the desired units (\( \text {m}^3\) is in the top of our original fraction, so we chose the conversion factor with \( \text {m}^3\) in the bottom so they will cancel out).

Then cancel out the \( \text {m}^3\).

\(\displaystyle \frac{30\:\cancel{\text{m}^{3}}}{1}\times\frac{1\:\text{yd}^{3}}{0.7646\:\cancel{\text{m}^{3}}}\)

Next, multiply straight across:

\(\dfrac{30\times 1\:\text{yd}^{3}}{1\times0.7646}\)

Which equals to the following:

\(\dfrac{30\:\text{yd}^{3}}{0.7646}\)

Then divide 30 by 0.7646, which gives us the following:

\(39.24\:\text{yd}^{3}\)

So we need \(39.24\:\text{yards}^{3}\) of dirt to fill that volume.

\(\displaystyle \frac{340\:\text {mm}^{3}}{1} \times \frac{1\:\text{cm}^{3}}{1000\:\text{mm}^{3}} = .34\:\text{cm}^{3}\)

\(\displaystyle \frac{300,000\:\text {ft}^{3}}{1}\times\frac{0.0283\:\text{m}^{3}}{1\:\text{ft}^{3}}=8,490\:\text{m}^{3}\)
(Slight differences in rounding can cause the final answer to be off by a few numbers.)

Written Solution:
Step 1: Start with what you know: The room is 300,000 cubic feet

Step 2: Determine what you want to get in the end. (Figure out what the end units should be.): Cubic meters

Step 3: Determine what conversion factor(s) to use:


We know the following:
\(\text{1 ft} = 0.3048\; m\)



To determine how many cubic meters are in one cubic foot we start with the equation:
\(\text{1 ft} = 0.3048\; m\)

Then cube both sides of the equation:
\(\text{(1 ft)}^{3}\) = \(\text{(0.3840 m)}^{3}\)

Which gives us the following:
\(\text{1 ft}^{3}\) = \(\text{0.0283 m}^{3}\)

Step 4: Multiply by 1 in the form of the conversion factor that cancels out the unwanted units.

Since we have \(300,000\:\text{ft}^{3}\) we will multiply it by \(\dfrac{0.0283\:\text{m}^{3}}{1\:\text{ft}^{3}}\):

\(\displaystyle \frac{300,000\:\text{ft}^{3}}{1}\times\dfrac{0.0283\:\text{m}^{3}}{1\:\text{ft}^{3}}\)

Note that we chose the conversion factor that will enable us to cancel out the existing units and change them to the desired units (\(\text{ft}^{3}\) is on the top of our original fraction, so we chose the conversion factor with \(\text{ft}^{3}\) in the bottom so they will cancel out).

Then cancel out \(\text{ft}^{3}\):
\(\displaystyle \frac{300,000\:\cancel{\text{ft}^{3}}}{1}\times\frac{0.0283\:\text{m}^{3}}{1\:\cancel{\text{ft}^{3}}}\)

Then multiply straight across:
\(\displaystyle \frac{300,000\times0.0283\:\text{m}^{3}}{1\times1}\)

Which equals to the following:
\(8490\:\text{m}^{3}\)