### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : Volume Of A Rectangular Solid

If a cube is inches tall, what is its volume?

**Possible Answers:**

Not enough information provided.

**Correct answer:**

To find the volume of a cube, we multiply length by width by height, which can be represented with the forumla . Since a cube has equal sides, we can use for all three values.

### Example Question #1 : Volume Of A Rectangular Solid

What is the volume of a cube with a side length equal to inches?

**Possible Answers:**

**Correct answer:**

The volume of a a cube (or rectangular prism) can be solved using the following equation:

### Example Question #1 : Finding Volume Of A Cube

Give the volume of a cube with surface area 150 square inches.

**Possible Answers:**

**Correct answer:**

Let be the length of one edge of the cube. Since its surface area is 150 square inches, one face has one-sixth of this area, or square inches. Therefore, , and .

The volume is the cube of this, or cubic inches.

### Example Question #1 : Cubes

What is the volume of a cube in which the edge is equal to , and the value of is:

**Possible Answers:**

**Correct answer:**

First, the value of x must be solved for:

Given the edge of the cube is , plugging in the value of x results in . Thus, the area would be equal to this value cubed, which would result in 62.

Thus, 62 is the correct answer.

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

The length of a diagonal of one face of a cube is . Give the volume of the cube.

**Possible Answers:**

**Correct answer:**

Since a diagonal of a square face of the cube is, each side of each square has length .

Cube this to get the volume of the cube:

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

The distance from one vertex of a perfectly cubic aquarium to its opposite vertex is 1.5 meters. Give the volume of the aquarium in liters.

1 cubic meter = 1,000 liters.

**Possible Answers:**

The correct answer is not given among the other responses.

**Correct answer:**

The correct answer is not given among the other responses.

Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,

meters.

Cube this sidelength to get the volume:

cubic meters.

To convert this to liters, multiply by 1,000:

liters.

This is not among the given responses.

### Example Question #2 : Finding Volume Of A Cube

Give the volume of a cube with surface area 240 square inches.

**Possible Answers:**

**Correct answer:**

Let be the length of one edge of the cube. Since its surface area is 240 square inches, one face has one-sixth of this area, or square inches. Therefore, , and .

The volume is the cube of this, or cubic inches.

### Example Question #1 : Finding Volume Of A Rectangular Prism

An aquarium is shaped like a perfect cube; the perimeter of each glass face is meters. If it is filled to the recommended capacity, then, to the nearest hundred cubic liters, how much water will it contain?

**Possible Answers:**

Insufficient information is given to answer the question.

Note:

**Correct answer:**

A perfect cube has square faces; if a face has perimeter meters, then each side of each face measures one fourth of this, or meters. The volume of the tank is the cube of this, or

cubic meters.

Its capacity in liters is liters.

of this is

liters.

This rounds to liters, the correct response.

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

Your friend gives you a puzzle cube for your birthday. If the length of one edge is 5cm, what is the volume of the cube?

**Possible Answers:**

**Correct answer:**

Your friend gives you a puzzle cube for your birthday. If the length of one edge is 5cm, what is the volume of the cube?

To find the volume of a cube, use the following formula:

Where s is the side length.

Plug in what we know to get our answer:

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

A cube has a side length of , what is the volume of the cube?

**Possible Answers:**

**Correct answer:**

A cube has a side length of , what is the volume of the cube?

To find the volume of a cube, use the following formula:

Plug in our known side length and solve

Making our answer: