Finding the perimeter of a cube may seem a bit difficult since perimeters are generally associated with two-dimensional figures and a cube is a three-dimensional object. However, a cube can be considered as a collection of two-dimensional objects since each of its six faces is a square. Similar to how the perimeter of a square is equal to the sum of the lengths of its sides, the perimeter of a cube is equal to the sum of its separate sides, also known as the edges of the cube.
Here, we will learn about the formula that we can use to calculate the perimeter of a cube. In addition, we will look at some exercises in which we will apply this formula.
Formula to find the perimeter of a cube
The perimeter of a cube can be considered as the sum of the lengths of all the sides of the cube, also known as the edges. In a cube, we have 12 edges in total. Also, we know that a cube is a regular figure, which means that all 12 edges have the same length.
Therefore, considering all of this, we can obtain the following formula for the perimeter:
| $latex p=12a$ |
where a is the length of one of the edges of the cube.
Perimeter of a cube – Examples with answers
The following examples are solved using the formula for the perimeter of a cube detailed above. Each example has its respective solution, but it is recommended that you try to solve the problems yourself before looking at the answer.
EXAMPLE 1
A cube has edges of length 5 m. What is its perimeter?
Solution
We use the length $latex a=5$ in the perimeter formula:
$latex p=12a$
$latex p=12(5)$
$latex p=60$
The perimeter is equal to 60 m.
EXAMPLE 2
If a cube has edges of length 8 m, what is its perimeter?
Solution
We have the length $latex a = 8$, so we use this value in the perimeter formula:
$latex p=12a$
$latex p=12(8)$
$latex p=96$
The perimeter is equal to 96 m.
EXAMPLE 3
What is the perimeter of a cube that has edges of length 15 m?
Solution
We use the length $latex a=5$ in the perimeter formula:
$latex p=12a$
$latex p=12(15)$
$latex p=180$
The perimeter is equal to 180 m.
EXAMPLE 4
What is the length of the sides of a cube that has a perimeter of 120 m?
Solution
To find the length of the sides or edges, we have to use $latex p=120$ and solve for a:
$latex p=12a$
$latex 120=12a$
$latex a=10$
The sides are 10 m long.
EXAMPLE 5
How long are the edges of a cube that has a perimeter of 260 m?
Solution
We use the perimeter measure $latex p=260$ in the perimeter formula and solve for a:
$latex p=12a$
$latex 260=12a$
$latex a=21.67$
The length of the edges is 21.67 m.
Perimeter of a cube – Practice problems
Use the following problems to practice applying the formula for the perimeter of cubes. If you need help with this, you can look at the solved examples above.
See also
Interested in learning more about cubes? Take a look at these pages:
Jefferson Huera Guzman
Jefferson is the lead author and administrator of Neurochispas.com. The interactive Mathematics and Physics content that I have created has helped many students.
