Suppose a cube has a side length of 'n' units; calculate the surface area and explain the process.
user
Sure, I'd be happy to help you with that!

A cube is a three-dimensional shape with sides that are all equal in length. The surface area of a cube is the total area of all six faces, including top, bottom, front, back, and the left and right faces. To calculate the surface area, you need to add the area of all six faces.

Here's the formula to calculate the surface area of a cube:

Surface Area = 6 * (side length)^2

Let's break down this formula.

6: This number represents the total number of faces in a cube, which is six.

(Side length)^2: This represents the area of each face. The area of a square (face) is calculated by multiplying its length (side length) by its width (side length) or (length)^2.

So, when you multiply 6 by the square of the length of one side, you get the total surface area.

For example, if the side length of a cube is 5 units, then:

Surface Area = 6 * (5)^2 = 75 square units

So, the surface area of the cube is 75 square units.

I hope this helps! Let me know if you have any further questions.
assistant
Suppose a cube has a side length of 'n' units; calculate the surface area and explain the process.
user
Sure, I'd be happy to help with that!

The surface area of a cube is calculated by finding the total area of all its faces. A cube has six identical square faces, and the area of each square face is calculated by squaring the length of one side.

Here's the step-by-step process:

1. Find the area of one face of the cube. Since each face of a cube is a square, and the area of a square is side length squared (side × side), the area of one face would be n × n = n².

2. A cube has six faces, so to find the total surface area, you multiply the area of one face by six.

So, the surface area (SA) of the cube would be SA = 6 * n².

For example, if the side length (n) of the cube is 3 units, then the surface area would be 6 * 3² = 54 square units.
assistant