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:

• 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
\(\color{blue}{\text{ Total } = 64 + 64 + 27}\) = 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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Unit Conversions and Missing Sides

Many volume word problems add one extra step: changing units or working backward from the volume.

Example: A fish tank is 50 cm long, 30 cm wide and 40 cm tall. How many liters does it hold? V = 50 × 30 × 40 = 60,000 cm³. Divide by 1,000: the tank holds 60 liters.

Missing side: A box holds 360 in³. It is 10 in long and 6 in wide. How tall is it? 10 × 6 = 60, and 360 ÷ 60 = 6, so the box is 6 in tall. For a cube, take the cube root: a cube with volume 343 cm³ has sides of 7 cm, since 7 × 7 × 7 = 343.

Common Mistakes

• Mixing units, such as multiplying feet by inches. Convert first.
• Writing square units (ft²) instead of cubic units (ft³).
• Finding surface area when the question asks how much fits inside.
• Forgetting to count every object. Two identical rooms means adding that volume twice.
• Changing cubic units with a linear factor, like dividing cubic inches by 12 instead of 1,728.

Frequently Asked Questions

How do you solve volume of a cube word problems?

Find the side length, then multiply it by itself three times using V = s³. If a toy storage cube has 14 in sides, its volume is 14 × 14 × 14 = 2,744 in³. Read carefully: if the problem gives the area of one face instead of the side, take the square root of that area to find the side first.

How do you solve rectangular prism volume problems?

Pick out the length, width and height, make sure they use the same unit, and multiply with V = l × w × h. A fish tank 30 in long, 12 in wide and 16 in tall holds 30 × 12 × 16 = 5,760 in³. If one measurement is in feet and another in inches, convert before you multiply.

What is the difference between a cube and a cuboid in volume word problems?

A cube has all edges the same length, so V = s³. A cuboid, also called a rectangular prism, can have three different edge lengths, so V = l × w × h. Every cube is a special cuboid. A cube with 4 m edges holds 64 m³, while a 4 m by 2 m by 3 m cuboid holds 24 m³.

How do you find V using V = lwh if l = 3, w = 2 and h = 7?

Substitute the values and multiply: V = 3 × 2 × 7 = 42. In a word problem, label the answer in cubic units, such as 42 ft³ if the lengths were in feet. The order of multiplication does not matter, so start with the easiest pair: 3 × 2 = 6, then 6 × 7 = 42.

How do you solve complex volume problems?

Break the solid into simple boxes, find each volume, then add or subtract. An L-shaped room with a 9 ft ceiling can be split into a 10 ft by 8 ft part and a 6 ft by 4 ft part: 10 × 8 × 9 = 720 ft³ and 6 × 4 × 9 = 216 ft³, so the total is 936 ft³. For a box with a piece cut out, subtract the missing part.

What is the difference between volume and surface area in rectangular prism word problems?

Volume measures how much a solid holds, in cubic units, while surface area measures the total area of its outside faces, in square units. Filling a box with sand is a volume question; wrapping it in paper is a surface area question. For a 5 cm by 3 cm by 2 cm box, V = 30 cm³ and SA = 2(15 + 10 + 6) = 62 cm².

Related Topics

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