Back
Unit Conversions for Volume
> ... Math > Unit Conversions > Unit Conversions for Volume

Often, instead of using cubic inches or centimeters for volume, we use cups, quarts, or liters to measure volume. The following videos show, first, different conversion factors between measures of volume, and second, an example of a volume conversion.

Unit Conversions for Volume
Example of Using Unit Conversions for Volume

Steps for Volume Unit Conversions

2. Determine what you want to get in the end. (Figure out what the end units should be.)
3. Determine what conversion factor(s) to use. You may sometimes need more than one.
4. Multiply by 1 in the form of the conversion factor that cancels out the unwanted units.

Practice Problems

1. A wooden block has a volume of 210 cubic centimeters ($$\text {cm}^3$$). Use the fact that 1 inch is approximately equal to 2.54 cm to convert this volume to cubic inches ($$\text {in}^3$$). Round your answer to the nearest tenth.
$$\text{(1 in)}^{3}=\text{(2.54 cm)}^{3}$$ (
Solution
$$\displaystyle \frac{210\: \text{cm}^{3}}{1} \times \frac{1\:\text {in}^{3}}{16.387\:\text {cm}^{3}} = 12.8\:\text {in}^{3}$$
)
2. The Great Pyramid of Giza has a total volume of 91,227,778 cubic feet ($$\text {ft}^3$$). Use the fact that 1 foot is approximately equal to 0.3048 meters to convert this volume to cubic meters ($$\text {m}^3$$). Round your answer to the nearest whole number.
$$\text{(1 ft)}^3 = \text{(0.3048 m)}^3$$ (
Solution
$$\displaystyle \frac{91,227,778\:\text{ft}^{3}}{1} \times \frac{0.02832\:\text{m}^{3}}{1\:\text {ft}^{3}} = 2,583,283\:\text{m}^{3}$$
(Slight differences in rounding can cause the final answer to be off by a few numbers.)
)
3. A cup of milk has a volume of 350 cubic centimeters ($$\text {cm}^3$$). Use the fact that 1 milliliter is equal to 1 cubic centimeter to convert this volume to milliliters. $$1\:\text{ml}=1\:\text{cm}^{3}$$ (
Solution
$$\displaystyle \frac{350\:\text {cm}^{3}}{1} \times \frac{1\:\text {ml}}{1\:\text {cm}^{3}} = 350\:\text {ml}$$
)
4. Mary is landscaping her front yard and needs to fill an area with dirt that measures 2 m × 3 m × 5 m. Calculate the volume of dirt needed in cubic meters ($$\text {m}^3$$). Then convert the volume to cubic yards ($$\text {yd}^3$$) using the fact that 1 yard is approximately equal to 0.9144 meters. Round to the nearest hundredth.
$$2\:\text{m}\times3\:\text{m}\times5\:\text{m}=30\:\text{m}^{3}$$
$$\text{(1 yd)}^{3}=\text{(0.9144 m)}^{3}$$ (
Solution
$$\displaystyle \frac{30\:\text {m}^{3}}{1} \times \frac{1\:\text {yd}^{3}}{0.7646\:\text {m}^{3}} = 39.24\text {yd}^{3}$$

Written Solution:

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.
)
5. The volume of a gumball is about 340 cubic millimeters ($$\text {mm}^3$$). Use the fact that 10 millimeters equal 1 centimeter to convert this volume to cubic centimeters ($$\text {cm}^3$$). Round to the nearest hundredth. $$\text{(10 mm)}^{3}$$ = $$\text{(1 cm)}^{3}$$ (
Solution
$$\displaystyle \frac{340\:\text {mm}^{3}}{1} \times \frac{1\:\text{cm}^{3}}{1000\:\text{mm}^{3}} = .34\:\text{cm}^{3}$$
)
6. A storage facility has a large open room with a total volume of 300,000 cubic feet ($$\text {ft}^3$$). Use the fact that 1 foot is approximately equal to 0.3048 meters to convert this volume to cubic meters ($$\text {m}^3$$). Round your answer to the nearest whole number.
$$\text{(1 ft)}^{3}$$ = $$\text{(0.3048 m)}^{3}$$ (
Solution
$$\displaystyle \frac{300,000\:\text {ft}^{3}}{1}\times\frac{0.0283\:\text{m}^{3}}{1\:\text{ft}^{3}}=8,490\:\text{m}^{3}$$
(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:
$$8490\:\text{m}^{3}$$
)

Need More Help?

1. Study other Math Lessons in the Resource Center.
2. Visit the Online Tutoring Resources in the Resource Center.