## Example Questions

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

What is the volume of a rectangular box that is twice as long as it is high, and four times as wide as it is long?

2L2

8

5L

2L3

4L3

2L3

Explanation:

The box is 2 times as long as it is high, so H = L/2. It is also 4 times as wide as it is long, so W = 4L. Now we need volume = L * W * H = L * 4L * L/2 = 2L3.

### Example Question #2 : Cubes

What is the volume of a cube with a surface area of  ?      Explanation:

The surface area of a cube is merely the sum of the surface areas of the squares that make up its faces. Therefore, the surface area equation understandably is: , where is the side length of any one side of the cube. For our values, we know: Solving for , we get: or Now, the volume of a cube is defined by the simple equation: For , this is: ### Example Question #10 : Cubes

The volume of a cube is . If the side length of this cube is tripled, what is the new volume?      Explanation:

Recall that the volume of a cube is defined by the equation: , where is the side length of the cube.

Therefore, if we know that , we can solve: This means that .

Now, if we triple to , the new volume of our cube will be: ### Example Question #331 : Geometry

What is the volume of a cube with surface area of ?      Explanation:

Recall that the equation for the surface area of a cube is merely derived from the fact that the cube's faces are made up of squares. It is therefore: For our values, this is: Solving for , we get: , so Now, the volume of a cube is merely: Therefore, for , this value is: ### Example Question #332 : Geometry

A cube has a volume of 64, what would it be if you doubled its side lengths?      Explanation:

To find the volume of a cube, you multiple your side length 3 times (s*s*s).

To find the side length from the volume, you find the cube root which gives you 4 .

Doubling the side gives you 8 .

The volume of the new cube would then be 512 .

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