# High School Math : How to find the surface area of a cube

## Example Questions

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### Example Question #1 : How To Find The Surface Area Of A Cube

What is the surface area of a cube with a side length of 15?

Explanation:

To find the surface area of a cube we must count the number of surface faces and add the areas of each of them together.

In a cube there are 6 faces, each a square with the same side lengths.

In this example the side lengths is 15 so the area of each square would be

We then multiply this number by 6, the number of faces of the cube, to get

Our answer for the surface area is .

### Example Question #2 : How To Find The Surface Area Of A Cube

What is the surface area of a cube with a side length of ?

Explanation:

To find the surface area of a cube, we must count the number of surface faces and add the areas of each together. In a cube there are  faces, each a square with the same side lengths. In this example the side length is .

The area of a square is given by the equation . Using our side length, we can solve the area of once face of the cube.

We then multiply this number by , the number of faces of the cube to find the total surface area.

Our answer for the surface area is .

### Example Question #1 : How To Find The Surface Area Of A Cube

If the surface area of a cube equals 96, what is the length of one side of the cube?

5

6

4

3

4

Explanation:

The surface area of a cube = 6a2 where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube.

We have 96 = 6a→ a2 = 16, so that's the area of one face of the cube.

Solving we get √16, so a = 4

### Example Question #3 : How To Find The Surface Area Of A Cube

What is the surface area of a cube with a side length of ?

Explanation:

In order to find the surface area of a cube, use the formula .

### Example Question #2 : How To Find The Surface Area Of A Cube

What is the surface area, in inches, of a rectangular prism with a length of , a width of , and a height of ?

Explanation:

In order to find the surface area of a rectangular prism, use the formula .

However, all units must be the same. All of the units of this problem are in inches with the exception of .

Convert to inches.

Now, we can insert the known values into the surface area formula in order to calulate the surface area of the rectangular prism.

If you calculated the surface area to equal , then you utilized the volume formula of a rectangular prism, which is ; this is incorrect.

### Example Question #3 : How To Find The Surface Area Of A Cube

What is the surface area of a cube with a diagonal of ?

Explanation:

A few facts need to be known to solve this problem. Observe that the diagonal of the square face of the cube cuts it into two right isosceles triangles; therefore, the length of a side of the square to its diagonal is the same as an isosceles right triangle's leg to its hypotenuse: .

Rearrange an solve for .

Now, solve for the area of the cube using the formula .

### Example Question #4 : How To Find The Surface Area Of A Cube

This figure is a cube with one face having an area of 16 in2.

What is the surface area of the cube (in2)?

Explanation:

The surface area of a cube is the sum of the area of each face.  Since there are 6 faces on a cube, the surface area of the entire cube is .

### Example Question #5 : How To Find The Surface Area Of A Cube

A cube has a height of 4 feet. What is the surface area of the cube in feet?

Explanation:

To find the surface area of a cube, square the length of one edge and multiply the result by six:

### Example Question #6 : How To Find The Surface Area Of A Cube

The side length of a particular cube is . What is the surface area of this cube?

Explanation:

To find the surface of a cube, use the standard equation:

where  denotes the side length.

Plug in the given value for  to find the answer:

### Example Question #7 : How To Find The Surface Area Of A Cube

Sarah is wrapping a birthday present.  The box is a cube with sides of .  At a minimum, how many square feet of wrapping paper will she need?

Explanation:

Remember, .

For a cube:

Thus .

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