### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

What is the circumference of a circle with a radius equal to ?

**Possible Answers:**

**Correct answer:**

The circumference can be solved using the following equation:

### Example Question #1 : How To Find Circumference

The radius of a circle is . Give the circumference of the circle in terms of .

**Possible Answers:**

**Correct answer:**

The circumference can be calculated as , where is the radius of the circle.

### Example Question #2 : How To Find Circumference

The area of a circle is . Give the circumference of the circle in terms of .

Let .

**Possible Answers:**

**Correct answer:**

The area of a circle can be calculated as , where is the radius of the circle.

The circumference can be calculated as , where is the radius of the circle.

### Example Question #3 : How To Find Circumference

What is the circumference of a circle with a radius of ?

**Possible Answers:**

**Correct answer:**

The circumference can be solved using the following equation:

Where represents the radius. Therefore, when we substitute our radius in we get:

### Example Question #5 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

The perimeter of a given rectangle is equal to the circumference of a given circle. The circle has radius inches; the width of the rectangle is inches. What is the length of the rectangle?

**Possible Answers:**

inches

inches

inches

inches

inches

**Correct answer:**

inches

The circumference of a circle with radius inches is

inches.

The perimeter of the rectangle is therefore inches. To find its length, substitute and into the equation and solve for :

inches

### Example Question #4 : How To Find Circumference

The area of the shaded region in the above diagram is . Give the circumference of the circle.

**Possible Answers:**

**Correct answer:**

The shaded region is an sector; this represents

of the circle. The area of the region is therefore

,

where is the radius. Setting and solving for :

The circumference of a circle is its radius multiplied by , or

### Example Question #4 : How To Find Circumference

A circle has a radius of 5 miles, what is its circumference?

**Possible Answers:**

**Correct answer:**

A circle has a radius of 5 miles, what is its circumference?

To find circumference, use the following formula:

Where r is our radius.

Plug in 5 miles to get our answer:

### Example Question #5 : How To Find Circumference

While mailing some very important letters, you decide to use your circular rubber stamp. If the stamp has a radius of 3.5 cm, what is the circumference of the stamping surface?

**Possible Answers:**

Cannot be determined from the information provided.

**Correct answer:**

While mailing some very important letters, you decide to use your circular rubber stamp. If the stamp has a radius of 3.5 cm, what is the circumference of the stamping surface?

Find circumference via the following:

Where r is our radius, which is 3.5 cm.

### Example Question #6 : How To Find Circumference

You have a circular window in your vacation room. It has a radius of 9 inches. What is the circumference of the window?

**Possible Answers:**

**Correct answer:**

You have a circular window in your vacation room. It has a radius of 9 inches. What is the circumference of the window?

Begin with the formula for circumference of a circle.

Next, plug in our "r" and solve for C

So, we have our answer!

### Example Question #7 : How To Find Circumference

Find the circumference of a circle with a radius of 4cm.

**Possible Answers:**

**Correct answer:**

To find the circumference of a circle, we will use the following formula:

where *r* is the radius of the circle.

Now, we know the radius of the circle is 4cm.

Knowing this, we can substitute into the formula. We get