### All High School Math Resources

## Example Questions

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

A cube has a surface area of units squared. What is its volume?

**Possible Answers:**

units cubed

units cubed

units cubed

units cubed

**Correct answer:**

units cubed

Since a cube has square faces and the surface area of each face is given by multiplying the length of one side of the square face by itself, the equation for the surface area of a cube is , where is the length of one side of one face (i.e., one edge of the cube). Find the length of one side/edge of the given cube by setting the given surface area equal to :

units

The volume of a cube is , where is the length of one of the cube's edges. Substituing the solution to the previous equation for in the volume equation gives the volume of the cube:

units cubed

### Example Question #61 : Solid Geometry

Find the volume of the following cube:

**Possible Answers:**

**Correct answer:**

The formula for the volume of a cube is

,

where is the side of the cube.

Plugging in our values, we get:

### Example Question #61 : Solid Geometry

What is the difference in volume between a sphere with radius x and a cube with a side of 2x? Let π = 3.14

**Possible Answers:**

5.28x^{3 }

8.00x^{3}

4.18x^{3 }

3.82x^{3}

6.73x^{3 }

**Correct answer:**

3.82x^{3}

V_{cube} = s^{3} = (2x)^{3} = 8x^{3}

V_{sphere} = 4/3 πr^{3} = 4/3•3.14•x^{3} = 4.18x^{3 }

### Example Question #151 : Geometry

The density of gold is and the density of glass is . You have a gold cube that is in length on each side. If you want to make a glass cube that is the same weight as the gold cube, how long must each side of the glass cube be?

**Possible Answers:**

**Correct answer:**

Weight = Density * Volume

Volume of Gold Cube = side^{3}= x^{3}

Weight of Gold = 16 g/cm^{3 }* x^{3}

Weight of Glass = 3/cm^{3} * side^{3}

Set the weight of the gold equal to the weight of the glass and solve for the side length:

16* x^{3} = 2 * side^{3}

side^{3} = 16/2* x^{3 }= 8 x^{3}

Take the cube root of both sides:

side = 2x

### Example Question #37 : Solid Geometry

A cube has edges that are three times as long as those of a smaller cube. The volume of the bigger cube is how many times larger than that of the smaller cube?

**Possible Answers:**

**Correct answer:**

If we let represent the length of an edge on the smaller cube, its volume is .

The larger cube has edges three times as long, so the length can be represented as . The volume is , which is .

The large cube's volume of is 27 times as large as the small cube's volume of .

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

If a cube has its edges increased by a factor of 5, what is the ratio of the new volume to the old volume?

**Possible Answers:**

**Correct answer:**

A cubic volume is . Let the original sides be 1, so that the original volume is 1. Then find the volume if the sides measure 5. This new volume is 125. Therefore, the ratio of new volume to old volume is 125: 1.

### Example Question #62 : Solid Geometry

A cube has a side length of meters. What is the volume of the cube?

**Possible Answers:**

**Correct answer:**

The formula for the volume of a cube is:

Since the length of one side is meters, the volume of the cube is:

meters cubed.

### Example Question #61 : Solid Geometry

If the length of the side of a cube is , which expression represents the volume of the cube?

**Possible Answers:**

none of the other answers

**Correct answer:**

The formula for the volume of the cube is

Plugging that into Volume equation, we find and

Thus, the answer is 512x^{6}

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

A tank measuring 3in wide by 5in deep is 10in tall. If there are two cubes with 2in sides in the tank, how much water is needed to fill it?

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Pyramids

What is the volume of a pyramid with a height of and a square base with a side length of ?

**Possible Answers:**

**Correct answer:**

To find the volume of a pyramid we must use the equation

We must first solve for the area of the square using

We plug in and square it to get

We then plug our answer into the equation for the pyramid with the height to get

We multiply the result to get our final answer for the volume of the pyramid

.

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