prove the surface area of 3D cube
Answers
Answer:
The surface area of a polyhedron is equal to the sum of the area of all of its faces. Said another way, the surface area is the total area covered by the net of a polyhedron. Let's take a look at a cube.
As you already know, a cube has six square faces. If each of those faces is 3 inches by 3 inches, then the area of each face is 3 × 3 = 9 square inches. And since there are six of them, the total surface area is 9 + 9 + 9 + 9 + 9 + 9 = 54 square inches.
To find the surface area of any shape, you can follow the process described below:
Draw a net of the polyhedron.
Calculate the area of each face.
Add up the area of all the faces.
But for many polyhedra, there are formulas that can be used to find the total surface area. For instance, the formula for the surface area of a cube is:
SAcube = 6s2
where s is the side length of the square faces.
Diagram of a 3x3x3 cube.
Diagram of a 3x3x3 cube, flattened.