How to Find the Volume and Surface Area of Rectangular Prisms? (+FREE Worksheet!)

A rectangular prism is the 3-D shape you encounter every day — think of a cereal box, a brick, or a room. It has six rectangular faces, three pairs of parallel and congruent faces, and all right-angle corners. On the GED Math test you need to know how to find its volume (interior space) and its surface area (total face area). Both formulas are straightforward once you know the three dimensions.

What Is a Rectangular Prism?

A rectangular prism (also called a cuboid) is a solid with:

• 6 rectangular faces
• 12 edges
• 8 vertices (corners)
• Three dimensions: length (l), width (w), and height (h)

When \(\color{blue}{l = w = h}\), the rectangular prism becomes a cube.

Formulas for a Rectangular Prism

Volume of a Rectangular Prism

\(\color{blue}{V = l \times w \times h}\)

Volume is measured in cubic units (cm³, in³, ft³, etc.).

Surface Area of a Rectangular Prism

\(\color{blue}{\text{ SA } = 2(\text{ lw } + \text{ lh } + \text{ wh })}\)

Surface area is measured in square units (cm², in², ft², etc.).

The formula adds the areas of all 6 faces: \(\color{blue}{\text{ top } + \text{ bottom }}\) (lw each), \(\color{blue}{\text{ front } + \text{ back }}\) (lh each), and two sides (wh each).

Step-by-Step Summary

1. Identify the length, width, and height from the problem or diagram.
2. For volume: multiply \(\color{blue}{l \times w \times h}\).
3. For surface area: compute lw, lh, and wh; add them; multiply by 2.
4. Label the answer with the correct units (cubic for volume, square for SA).

Watch: Volume of Rectangular Prisms (Video Lesson)

Math with Mr. J explains the volume formula with step-by-step worked examples:

Worked Examples

Example 1: A rectangular prism has \(\color{blue}{l = 6}\) cm, \(\color{blue}{w = 4}\) cm, \(\color{blue}{h = 3}\) cm. Find the volume and surface area.

\(\color{blue}{V = 6 \times 4 \times 3}\) = 72 cm³
\(\color{blue}{\text{ SA } = 2(6\times 4 + 6\times 3 + 4\times 3) = 2(24 + 18 + 12) = 2(54)}\) = 108 cm²

Example 2: A box measures 8 \(\color{blue}{\text{ in } \times 5}\) \(\color{blue}{\text{ in } \times 2}\) in. Find its volume and surface area.

\(\color{blue}{V = 8 \times 5 \times 2}\) = 80 in³
\(\color{blue}{\text{ SA } = 2(8\times 5 + 8\times 2 + 5\times 2) = 2(40 + 16 + 10) = 2(66)}\) = 132 in²

Example 3: Find the volume of a prism with \(\color{blue}{l = 10}\) m, \(\color{blue}{w = 3}\) m, \(\color{blue}{h = 4}\) m.

\(\color{blue}{V = 10 \times 3 \times 4}\) = 120 m³

Example 4: A fish tank is 7 \(\color{blue}{\text{ ft } \times 2}\) \(\color{blue}{\text{ ft } \times 5}\) ft. How many cubic feet of water does it hold?

\(\color{blue}{V = 7 \times 2 \times 5}\) = 70 ft³

More Practice: Surface Area for GED Math (Video)

This GED-focused lesson walks you through finding the surface area of a rectangular prism:

Exercises

1. A rectangular prism has \(\color{blue}{l = 5}\) ft, \(\color{blue}{w = 3}\) ft, \(\color{blue}{h = 2}\) ft. Find the volume.
2. Find the surface area of a prism with \(\color{blue}{l = 9}\) cm, \(\color{blue}{w = 4}\) cm, \(\color{blue}{h = 6}\) cm.
3. A box has \(\color{blue}{V = 120}\) in³, \(\color{blue}{l = 10}\) in, \(\color{blue}{w = 4}\) in. Find h.
4. Find the volume of a prism with \(\color{blue}{l = 12}\) m, \(\color{blue}{w = 5}\) m, \(\color{blue}{h = 3}\) m.
5. Find the surface area of a prism with \(\color{blue}{l = 7}\) in, \(\color{blue}{w = 2}\) in, \(\color{blue}{h = 5}\) in.
6. A shipping container is 40 \(\color{blue}{\text{ ft } \times 8}\) \(\color{blue}{\text{ ft } \times 8}\) ft. What is its volume?

Answers

1. \(\color{blue}{V = 5 \times 3 \times 2}\) = 30 ft³
2. \(\color{blue}{\text{ SA } = 2(9\times 4 + 9\times 6 + 4\times 6) = 2(36 + 54 + 24) = 2(114)}\) = 228 cm²
3. \(\color{blue}{h = 120 \div (10 \times 4) = 120 \div 40}\) = 3 in
4. \(\color{blue}{V = 12 \times 5 \times 3}\) = 180 m³
5. \(\color{blue}{\text{ SA } = 2(7\times 2 + 7\times 5 + 2\times 5) = 2(14 + 35 + 10) = 2(59)}\) = 118 in²
6. \(\color{blue}{V = 40 \times 8 \times 8}\) = 2,560 ft³

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Frequently Asked Questions

What is the volume formula for a rectangular prism?

The volume of a rectangular prism is V = l × w × h: length times width times height. It counts the cubic units that fill the box. A box that is 8 inches long, 5 inches wide, and 3 inches tall holds 8 × 5 × 3 = 120 cubic inches. You can also think of it as base area times height: 40 × 3 = 120.

How do you find the surface area of a rectangular prism?

Add the areas of all six faces, which come in three matching pairs: SA = 2lw + 2lh + 2wh. For a prism 8 by 5 by 3, the faces are 40, 24, and 15, so SA = 2(40 + 24 + 15) = 2(79) = 158 square units. GED and middle school questions often use this for wrapping paper or painting a box.

How many faces, edges and vertices does a rectangular prism have?

A rectangular prism has 6 faces, 12 edges, and 8 vertices. The faces are all rectangles in 3 pairs of opposite, congruent faces. You can check the numbers with Euler’s formula for solids, faces + vertices − edges = 2: here 6 + 8 − 12 = 2.

Is a rectangular prism a cuboid?

Yes. Cuboid and rectangular prism are two names for the same solid: six rectangular faces meeting at right angles. Cuboid is more common in British and Indian textbooks, while US classes and the GED usually say rectangular prism. The formulas V = lwh and SA = 2lw + 2lh + 2wh work the same under either name.

Are rectangular prisms cubes?

Not usually. A cube is a special rectangular prism whose length, width, and height are all equal, so every face is a square. A shoebox is a rectangular prism but not a cube. For a cube with edge 4, the rectangular prism formulas simplify: V = 4³ = 64 cubic units and SA = 6 × 4² = 96 square units.

What does the net of a rectangular prism look like?

A net is the flat pattern you would get by unfolding the box: six rectangles in three matching pairs, often arranged in a cross or T shape. Labeling each rectangle with its dimensions turns the net into a surface area check, because the total area of the net equals the prism’s surface area.

Related Topics

• Cubes
• Word Problems Involving Volume of Cubes and Rectangular Prisms
• Finding Area of Compound Figures
• Area of a Parallelogram
• Polygons