How to Find Volume and Surface Area of Cubes

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Volume and Surface Area

A cube has one edge length, usually called $s$. Volume measures the space inside; surface area measures the outside covering.

$V = s^3$

$SA = 6s^2$

Volume uses cubic units, while surface area uses square units.

Example

If $s = 4$, then $V = 4^3 = 64$ cubic units and $SA = 6(4^2) = 96$ square units.

For a refresher on volume only, see Volume of Cubes.

volume and Surface Area of Cubes

Think of this lesson as more than a rule to memorize. volume and Surface Area of Cubes is about three-dimensional measurement, volume, and surface area. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.

Geometry formulas work because they measure a specific feature: length around, space inside, or space enclosed by a solid. Match the question to the measurement first.

Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.

Sketch or label the shape.
Decide whether the question asks for length, area, volume, or surface area.
Substitute values into the matching formula.
Keep units squared for area and cubed for volume.

A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.

Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.

When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.

On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.

Free printable Worksheets

Exercises for Volume and Surface Area of Cubes

1) A cube has edge length $4$ units. Find its volume.

2) A cube has side length $5$ units. Find its surface area.

3) A cube has edge length $6$ units. Find both volume and surface area.

4) A cube has volume $27$. Find its surface area.

5) A cube has surface area $294$. Find its volume.

6) A cube has side length $6$ units. Find its surface area.

7) A cube has side length $8$ cm. Find its surface area.

8) A cube has volume $512$. Find its surface area.

9) The total length of all 12 edges is $60$. Find volume and surface area.

10) A cube has surface area $600$. Find its volume.

11) A cube's side increases from $4$ to $7$. By how much does volume increase?

12) A cube has edge length $9$ units. Find both volume and surface area.

13) A cube of edge $10$ is cut into cubes of edge $2$. How many small cubes are formed?

14) A cube has edge length $\frac{5}{2}$ units. Find both volume and surface area.

15) A cube's volume is multiplied by $64$. By what factor is its surface area multiplied?

16) Painting a cube costs $\$0.08$ per square centimeter. The side length is $15$ cm. What is the cost?

17) For a cube, the numerical value of volume equals the numerical value of surface area. Find the side length.

18) Four separate cubes each have side length $3$. Find their combined surface area.

19) One face of a cube has area $81$. Find the cube's volume.

20) A $8\times9\times24$ prism and a cube have the same volume. Find the cube's surface area.

Answers

1) Use $V = s^3$.
Substitute: $V = 4^3$.
Compute: $64$.
Answer: $\color{red}{64\ \text{units}^3}$

2) Use $SA = 6s^2$.
Compute $6(5^2) = 150$.
Answer: $\color{red}{150\ \text{units}^2}$

3) Volume: $6^3 = 216$.
Surface area: $6(6^2) = 216$.
Answer: $\color{red}{V = 216,\ SA = 216}$

4) Edge is $3$ because $3^3 = 27$.
Surface area is $6(3^2) = 54$.
Answer: $\color{red}{54\ \text{square units}}$

5) Set $294 = 6s^2$.
Then $s^2 = 49$, so $s = 7$.
Volume is $7^3 = 343$.
Answer: $\color{red}{343\ \text{cubic units}}$

6) Use $SA = 6s^2$.
Compute $6(6^2) = 216$.
Answer: $\color{red}{216\ \text{units}^2}$

7) Use $SA = 6s^2$.
Compute $6(8^2) = 384$.
Answer: $\color{red}{384\ \text{cm}^2}$

8) Edge is $8$.
Surface area is $6(8^2) = 384$.
Answer: $\color{red}{384\ \text{square units}}$

9) Each edge is $60\div12 = 5$.
Volume is $125$; surface area is $150$.
Answer: $\color{red}{V = 125,\ SA = 150}$

10) Set $600 = 6s^2$.
Then $s = 10$.
Volume is $1000$.
Answer: $\color{red}{1000\ \text{cubic units}}$

11) Original volume: $64$.
New volume: $343$.
Increase: $279$.
Answer: $\color{red}{279\ \text{cubic units}}$

12) Volume: $9^3 = 729$.
Surface area: $6(9^2) = 486$.
Answer: $\color{red}{V = 729,\ SA = 486}$

13) Large volume: $1000$.
Small volume: $8$.
Number: $125$.
Answer: $\color{red}{125}$

14) Volume: $\frac{5}{2}^3 = \frac{125}{8}$.
Surface area: $6(\frac{5}{2}^2) = \frac{75}{2}$.
Answer: $\color{red}{V = \frac{125}{8},\ SA = \frac{75}{2}}$

15) Length factor is $4$ because $4^3 = 64$.
Surface area factor is $4^2 = 16$.
Answer: $\color{red}{16}$

16) Surface area: $6(15^2) = 1350$.
Cost: $1350\cdot0.08 = 108$.
Answer: $\color{red}{\$108}$

17) Set $s^3 = 6s^2$.
Divide by $s^2$ because $s > 0$.
Then $s = 6$.
Answer: $\color{red}{6\ \text{units}}$

18) One cube: $6(3^2) = 54$.
Four cubes: $4\cdot54 = 216$.
Answer: $\color{red}{216\ \text{square units}}$

19) Since $s^2 = 81$, $s = 9$.
Volume is $9^3 = 729$.
Answer: $\color{red}{729\ \text{cubic units}}$

20) Volume is $8\cdot9\cdot24 = 1728$.
Cube edge is $12$.
Surface area is $6(12^2) = 864$.
Answer: $\color{red}{864\ \text{square units}}$

How to Find Volume and Surface Area of Cubes