How to Calculate the Total Area of a Cube

2024 Author: Samantha Chapman | [email protected]. Last modified: 2023-12-17 09:13

The surface of a solid is the sum of the extension of all the faces present outside it. The faces of a cube are all six congruent. Consequently, to find the total area of a cube, all you have to do is find the area of a single face of the cube and multiply it by six. If you want to know how to find the measurement of the total area of a cube, just follow these steps.

Steps

Method 1 of 2: Knowing the Length of an Edge

Step 1. Try to understand that the measurement of the total surface of a cube is made up of the area of its six faces

Since they are all congruent, we can find the area of a face and multiply it by six to get the measurement of the total area. The surface can be found using a simple formula: 6 x s², where "s" represents the edge of the cube.

Step 2. Find the surface of a cube face:

if "s" represents the length of the edge of a cube, calculate s². This means that you can multiply length by width to find its area: in a cube the two dimensions are identical. If "s" is equal to 4 cm, the area of one face measures (4 cm)² or 16 cm². Remember to put your answer in squared units.

Step 3. Multiply the area of the cube face by six:

now all you have to do is multiply this number by six. 16 cm² x 6 = 96 cm². The total surface area of the cube measures 96 cm².

Method 2 of 2: Knowing only the Volume

Step 1. Start with the volume of the cube

Suppose the volume of the cube is 125 cm³.

Step 2. Find the cube root of the volume

To find the cube root of the volume, just look for that number which, raised to the cube, gives the volume or you can use the calculator. The number will not always be an integer. In this case, the number 125 is a perfect cube and its cube root is 5, because 5 x 5 x 5 = 125. So, "s" is 5.

Step 3. Insert this result into the formula to find the measure of the total area of a cube

Now that you know the length of the edge, just enter it into the formula to find the total area of a cube: 6 x s². Since the length of an edge is 5 cm, just enter it in the formula like this: 6 x (5 cm)².

Step 4. Solve

Just do the math: 6 x (5cm)² = 6 x 25 cm² = 150 cm².