How to Find the Surface Area of a Cube

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posted on 15 years ago — updated on 1 second ago

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The surface area of an object is the combined area of all of the sides on its surface. All six sides of a cube are congruent, so to find the surface area of a cube, all you have to do is find the surface area of one side of the cube and then multiply it by six. If you want to know how to find the surface area of a cube, just follow these steps.

Steps

Calculating the Surface Area Knowing the Length of One Side

Understand that the surface area of a cube is made up of the areas of its six faces. Since all of the faces of a cube are congruent, we can just find the area of one face and multiply it by 6 to get the total surface area. The surface area can be found by using a simple formula: 6 x s, where "s" represents a side of the cube.

Find the area of one side of the cube. To find the area of one side of the cube, you need to find "s," which represents the side length of a cube, and then find s. This really means that you'll be multiplying the length of the cube's side times its width to find its area -- the length and width of a cube's side just happen to be the same. If one side of the cube, or "s," is equal to 4 centimeter (1.6 in), then the area of the side of the cube is (4 cm), or 16 cm. Remember to state your answer in square units.

Multiply the area of the side of the cube by 6. Now that you've found the area of one side of the cube, all you have to do to find the surface area is to multiply this number by 6. 16 cm x 6 = 96 cm. The surface area of the cube is 96 cm.

Calculating the Surface Area Knowing the Volume

Find the volume of the cube. Let's say that the volume of the cube is 125 cm.

Find the cube root of the volume. To find the cube root of the volume, just look for a number that can be cubed to become the volume, or use your calculator. The number won't always be a whole number. In this case, with the number 125 is a perfect cube, and its cube root is 5, because 5 x 5 x 5 = 125. So, "s," or one side of the cube, is 5.

Plug this answer into the formula for finding the surface area of a cube. Now that you know the length of one side of a cube, just plug it into the formula for finding the surface area of a cube: 6 x s. Since the length of one side is 5 centimeter (2.0 in), just plug it into the formula like this: 6 x (5 cm).