Surface Area of a Cube Calculator

Published on: July 14, 2024
Final Answer: Free • Full Steps: Plus

This Surface Area of a Cube Calculator finds the total area of the outside of a cube from the length of one edge, and shows the working line by line. Every face of a cube is a square built on the same edge, and a cube has six of them, so the area of one face is worked out first and then counted six times. The answer is written in square units. Following the same pattern every time is what makes the surface area of a cube easy to check and repeat.

Wireframe cube labeled a

In the diagram, each edge is labeled \(a\).

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the edge length into the formula.
  4. Square the edge length to get the area of one face.
  5. Multiply by six to get the surface area.

Formula:

\(SA = 6a^{2}\)
See Example 1 Hide Example 1

Problem

\(a = 7\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the edge length into the formula.
  4. Square the edge length to get the area of one face.
  5. Multiply by six to get the surface area.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the surface area of a cube whose edge length is \(a = 7\).

\(a = 7\)

Step 2

Step 2 - Write the formula.

In this problem: Every face of a cube is a square on the same edge, and a cube has six faces, so the surface area is the area of one face counted six times.

\(SA = 6a^{2}\)

Step 3

Step 3 - Substitute the edge length into the formula.

In this problem: Replacing \(a\) with \(7\) in \(SA = 6a^{2}\) gives \(SA = 6 \times 7^{2}\).

\(SA = 6 \times 7^{2}\)

Step 4

Step 4 - Square the edge length to get the area of one face.

In this problem: Squaring the edge length gives the area of one face: \(7^{2} = 7 \times 7 = 49\).

\(SA = 6 \times 49\)

Step 5

Step 5 - Multiply by six to get the surface area.

In this problem: Counting that face six times gives \(6 \times 49 = 294\).

\(SA = 6 \times 49 = 294\)

Final Answer

\(SA = 294\)
See Example 2 Hide Example 2

Problem

\(a = 1.5\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the edge length into the formula.
  4. Square the edge length to get the area of one face.
  5. Multiply by six to get the surface area.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the surface area of a cube whose edge length is \(a = 1.5\).

\(a = 1.5\)

Step 2

Step 2 - Write the formula.

In this problem: Every face of a cube is a square on the same edge, and a cube has six faces, so the surface area is the area of one face counted six times.

\(SA = 6a^{2}\)

Step 3

Step 3 - Substitute the edge length into the formula.

In this problem: Replacing \(a\) with \(1.5\) in \(SA = 6a^{2}\) gives \(SA = 6 \times 1.5^{2}\).

\(SA = 6 \times 1.5^{2}\)

Step 4

Step 4 - Square the edge length to get the area of one face.

In this problem: Squaring the edge length gives the area of one face: \(1.5^{2} = 1.5 \times 1.5 = 2.25\).

\(SA = 6 \times 2.25\)

Step 5

Step 5 - Multiply by six to get the surface area.

In this problem: Counting that face six times gives \(6 \times 2.25 = 13.5\).

\(SA = 6 \times 2.25 = 13.5\)

Final Answer

\(SA = 13.5\)

Example Problems

Click one to load it into the box and solve it.