How to Find the Surface Area of a Cube: 7 Steps (with Pictures)

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How to Find the Surface Area of a Cube: 7 Steps (with Pictures)
How to Find the Surface Area of a Cube: 7 Steps (with Pictures)

Video: How to Find the Surface Area of a Cube: 7 Steps (with Pictures)

Video: How to Find the Surface Area of a Cube: 7 Steps (with Pictures)
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The surface area of an object is the combined area of all the sides of the object's surface. The six sides of the cube are congruent, so to find the surface area of the cube we simply need to find the surface area of one side of the cube and then multiply by six. To know how to find the surface area of a cube, follow these steps.

Step

Method 1 of 2: If the Length of One Side is Known

Find the Surface Area of a Cube Step 1
Find the Surface Area of a Cube Step 1

Step 1. Understand that the surface area of a cube is made up of the areas of the six faces of the cube

Since all faces of the cube are congruent, we can find the area of one face and multiply by 6 to get the total surface area. The surface area can be found using the simple formula: 6xs2, "s" is the side of the cube.

Find the Surface Area of a Cube Step 2
Find the Surface Area of a Cube Step 2

Step 2. Find the area of one side of the cube

To find the area of one side of the cube, find "s" which is the length of the side of the cube, then find s2. This means that we will multiply the length of the side of the cube by the width to find its area. The length and width of the side of the cube happen to be the same. If one side of the cube or "s" is 4 cm, then the area of the side of the cube is (4 cm)2, or 16 cm2. Remember to state the answer in square units.

Find the Surface Area of a Cube Step 3
Find the Surface Area of a Cube Step 3

Step 3. Multiply the side area of the cube by 6

We already know the area of one side of the cube, and now we will find the surface area by multiplying this number by 6. 16 cm2x6 = 96 cm2.

Method 2 of 2: If Only the Volume is Known

Find the Surface Area of a Cube Step 4
Find the Surface Area of a Cube Step 4

Step 1. Find the volume of the cube. Let's say the volume of the cube is 125 cm3.

Find the Surface Area of a Cube Step 5
Find the Surface Area of a Cube Step 5

Step 2. Find the cube root of the volume

To find the cube root of a volume, simply look for a number that can be squared, or use a calculator. The result is not always an integer. In this case, 125 is a cube, and the cube root is 5, because 5x5x5 = 125. So the "s" or one of the sides of the cube, is 5.

Find the Surface Area of a Cube Step 6
Find the Surface Area of a Cube Step 6

Step 3. Plug this answer into the formula to find the surface area of a cube

Now that the length of one side of the cube is known, simply plug it into the formula to find the surface area of the cube: 6 x s2. Since one side is 5 cm long, simply plug it into the formula like this: 6 x (5 cm)2.

Find the Surface Area of a Cube Step 7
Find the Surface Area of a Cube Step 7

Step 4. Calculate

By math, 6 x (5 cm)2 = 6 x 25 cm2 = 150 cm2.

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