Word Problems Involving Volume of Cubes and Rectangular Prisms

Volume word problems on the GED test describe real-life containers, rooms, or packages and ask how much space they hold. The key is identifying whether the object is a cube or a rectangular prism, pulling out the right dimensions, and plugging them into the correct formula. This lesson gives you a reliable strategy plus plenty of practice.

What You Need to Know

Two formulas cover all GED volume problems for these shapes:

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• Cube: \(\color{blue}{V = s^{3}}\)   (\(\color{blue}{s = \text{ side }}\) length, all sides equal)
• Rectangular Prism: \(\color{blue}{V = l \times w \times h}\)   (\(\color{blue}{\text{ length } \times \text{ width } \times \text{ height }}\))

Read each problem carefully. Look for the word cubic or units like ft³, m³, or in³ as a sign that volume is involved.

Problem-Solving Strategy

Step-by-Step Approach

1. Read the problem and identify what shape is described.
2. List the given dimensions (length, width, height, or side).
3. Write the correct formula: \(\color{blue}{V = s^{3}}\) or \(\color{blue}{V = \text{ lwh }}\).
4. Substitute the values and calculate.
5. Label the answer with cubic units.

Common Key Words

• “capacity,” “holds,” “fills,” “interior space” → volume
• “box,” “tank,” “container,” “room,” “crate” → rectangular prism
• “cube-shaped,” “each side,” “all sides equal” → cube

Step-by-Step Summary

1. Identify the shape (cube or rectangular prism).
2. Extract the dimensions from the problem text.
3. Apply \(\color{blue}{V = s^{3}}\) (cube) or \(\color{blue}{V = \text{ lwh }}\) (rectangular prism).
4. Compute and include correct cubic units in the answer.

Watch: GED Math Volume of 3-D Shapes (Video Lesson)

This GED-specific lesson covers everything you need to know about volume for the test:

Worked Examples

Example 1: A shipping box measures 12 in long, 8 in wide, and 5 in tall. What is its volume?

Shape: rectangular prism
\(\color{blue}{V = l \times w \times h = 12 \times 8 \times 5}\) = 480 in³

Example 2: A cube-shaped storage box has a side length of 6 ft. How much space does it hold?

Shape: cube
\(\color{blue}{V = s^{3} = 6^{3} = 6 \times 6 \times 6}\) = 216 ft³

Example 3: A fish tank is 30 cm long, 12 cm wide, and 18 cm tall. How many cubic centimeters of water can it hold?

\(\color{blue}{V = 30 \times 12 \times 18}\) = 6,480 cm³

Example 4: A warehouse has two identical cube-shaped rooms with \(\color{blue}{s = 4}\) m and one room with \(\color{blue}{s = 3}\) m. What is the combined volume?

Each large room: \(\color{blue}{4^{3} = 64}\) m³; small room: \(\color{blue}{3^{3} = 27}\) m³
\(\color{blue}{\text{ Total } = 64 + 27}\) = 91 m³

More Practice: Volume Word Problems (Video)

This video works through real-world volume word problems step by step:

Exercises

1. A gift box is 9 \(\color{blue}{\text{ in } \times 4}\) \(\color{blue}{\text{ in } \times 3}\) in. Find its volume.
2. A cube-shaped toy has a side length of 5 cm. How much space does it occupy?
3. A swimming pool is 20 ft long, 10 ft wide, and 4 ft deep. Find its volume.
4. A cube has a volume of 512 cm³. What is the side length?
5. A wooden crate is 15 \(\color{blue}{\text{ ft } \times 6}\) \(\color{blue}{\text{ ft } \times 4}\) ft. Find its volume in cubic feet.
6. Two cube boxes have side lengths 3 in and 4 in. What is their combined volume?

Answers

1. \(\color{blue}{V = 9 \times 4 \times 3}\) = 108 in³
2. \(\color{blue}{V = 5^{3}}\) = 125 cm³
3. \(\color{blue}{V = 20 \times 10 \times 4}\) = 800 ft³
4. \(\color{blue}{s^{3} = 512}\), \(\color{blue}{s = 8}\) → 8 cm
5. \(\color{blue}{V = 15 \times 6 \times 4}\) = 360 ft³
6. \(\color{blue}{3^{3} + 4^{3} = 27 + 64}\) = 91 in³

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Frequently Asked Questions

How do I know if a problem is asking for volume or surface area?

Volume problems use words like “holds,” “capacity,” “fills,” or “interior space,” and the answer will be in cubic units. Surface area problems use words like “covers,” “paints,” or “wraps,” and the answer will be in square units.

What if only one dimension is given for a cube-shaped object?

If all sides are equal, that one measurement is s, and \(\color{blue}{V = s^{3}}\). For example, a cube-shaped box with side 4 ft has \(\color{blue}{V = 4^{3} = 64}\) ft³.

Can the volume be in different units for the same problem?

The volume unit is always the cube of the length unit. If lengths are in inches, volume is in in³. If a problem mixes units (e.g., some in feet, some in inches), convert all to the same unit before calculating.

Related Topics

• Cubes
• Rectangular Prisms
• Finding Area of Compound Figures
• Converting, Comparing, Adding and Subtracting Mixed Customary Units
• Area of a Triangle