A cube is a rectangular solid whose length, width, and height are equal. See Volume and Surface Area of a Cube, below. Substituting, s for the length, width and height into the formulas for volume and surface area of a rectangular solid, we get:
Volume and Surface Area of a Cube
For any cube with sides of length
s,
example
A cube is
2.5 inches on each side. Find its 1. volume and 2. surface area.
Solution
Step 1 is the same for both 1. and 2., so we will show it just once.
Step 1. Read the problem. Draw the figure and
label it with the given information. |
 |
1. |
|
Step 2. Identify what you are looking for. |
the volume of the cube |
Step 3. Name. Choose a variable to represent it. |
let V = volume |
Step 4. Translate.
Write the appropriate formula. |
V=s3 |
Step 5. Solve. Substitute and solve. |
V=(2.5)3
V=15.625 |
Step 6. Check: Check your work. |
|
Step 7. Answer the question. |
The volume is 15.625 cubic inches. |
2. |
|
Step 2. Identify what you are looking for. |
the surface area of the cube |
Step 3. Name. Choose a variable to represent it. |
let S = surface area |
Step 4. Translate.
Write the appropriate formula. |
S=6s2 |
Step 5. Solve. Substitute and solve. |
S=6⋅(2.5)2
S=37.5 |
Step 6. Check: The check is left to you. |
|
Step 7. Answer the question. |
The surface area is 37.5 square inches. |
example
A notepad cube measures
2 inches on each side. Find its 1. volume and 2. surface area.
Answer:
Solution
Step 1. Read the problem. Draw the figure and
label it with the given information. |
 |
1. |
|
Step 2. Identify what you are looking for. |
the volume of the cube |
Step 3. Name. Choose a variable to represent it. |
let V = volume |
Step 4. Translate.
Write the appropriate formula. |
V=s3 |
Step 5. Solve the equation. |
V=23
V=8 |
Step 6. Check: Check that you did the calculations
correctly. |
|
Step 7. Answer the question. |
The volume is 8 cubic inches. |
2. |
|
Step 2. Identify what you are looking for. |
the surface area of the cube |
Step 3. Name. Choose a variable to represent it. |
let S = surface area |
Step 4. Translate.
Write the appropriate formula. |
S=6s2 |
Step 5. Solve the equation. |
S=6⋅22
S=24 |
Step 6. Check: The check is left to you. |
|
Step 7. Answer the question. |
The surface area is 24 square inches. |