### All High School Math Resources

## Example Questions

### 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?

**Possible Answers:**

5

3

4

6

**Correct answer:**

4

The surface area of a cube = 6a^{2} 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^{2 }→ a^{2} = 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 ?

**Possible Answers:**

**Correct answer:**

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

### Example Question #4 : 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 ?

**Possible Answers:**

**Correct answer:**

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

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

**Possible Answers:**

**Correct answer:**

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

This figure is a cube with one face having an area of 16 in^{2}.

What is the surface area of the cube (in^{2})?

**Possible Answers:**

**Correct answer:**

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 #7 : 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?

**Possible Answers:**

**Correct answer:**

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

### Example Question #8 : 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?

**Possible Answers:**

**Correct answer:**

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 #9 : 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?

**Possible Answers:**

**Correct answer:**

Remember, .

For a cube:

Thus .

### Example Question #41 : Solid Geometry

**Possible Answers:**

**Correct answer:**

### Example Question #42 : Solid Geometry

Find the surface area of the following cube:

**Possible Answers:**

**Correct answer:**

The formula for the surface area of a cube is

,

where is the length of the side.

Plugging in our values, we get: