### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : Circles

A circle has a radius of . What is the ratio of the diameter to the circumference?

**Possible Answers:**

**Correct answer:**

The information about the radius is unnecessary to the problem. The equation of the circumference is:

Therefore, the circumference is times larger than the diameter, and the ratio of the diameter to the circumference is:

### Example Question #2 : Circles

A circle has a radius of . What is the ratio of the diameter to the circumference?

**Possible Answers:**

**Correct answer:**

The information about the radius is unnecessary to the problem. The equation of the circumference is:

Therefore, the circumference is times larger than the diameter, and the ratio of the diameter to the circumference is:

### Example Question #1 : Circles

The area of a circle is . Give the diameter and radius of the circle.

**Possible Answers:**

diameter = , radius =

diameter = , radius =

diameter = , radius =

diameter = , radius =

diameter = , radius =

**Correct answer:**

diameter = , radius =

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

To find the diameter, multiply the radius by :

### Example Question #4 : Circles

If the area of a circle is equal to , then what is the diameter?

**Possible Answers:**

**Correct answer:**

If the area of a circle is equal to , then the radius is equal to .

This is because the equation for the area of a circle is .

Thus, .

Then the diameter is 12.

### Example Question #5 : Circles

The circumference of a circle is . Give the diameter of the circle.

**Possible Answers:**

**Correct answer:**

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

### Example Question #6 : Circles

If the value of a radius is , what is the value of the diameter if the value of ?

**Possible Answers:**

**Correct answer:**

If the value of a radius is , and the value of , then the radius will be equal to:

Given that the diameter is twice that of the radius, the diameter will be equal to:

This is equal to:

### Example Question #7 : Circles

A series of circles has the following radius values:

If the diameter is then calculated for this set, what would be the median diameter?

**Possible Answers:**

**Correct answer:**

The median is the middle number in a set when that set is ordered smalles to largest.

When is ordered smallest to largest, we get

Here, the median would be .

Given that a diameter is twice the radius, the diamater would be (twice the value of ).

### Example Question #8 : Circles

The circumference of a circle is . Give the diameter of the circle.

**Possible Answers:**

**Correct answer:**

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

### Example Question #9 : Circles

You have a circular lens with a circumference of , find the diameter of the lens.

**Possible Answers:**

**Correct answer:**

You have a circular lens with a circumference of , find the diameter of the lens.

Begin with the circumference of a circle formula.

Now, we know that

Because our radius is half of our diameter.

So, we can change our original formula to be:

Now, we can see that all we need to do is divide our circumference by pi to get our diameter.

Now plug in our known and solve:

So our answer is 16.67inches

### Example Question #10 : Circles

You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be .

What is the diameter of the crater?

**Possible Answers:**

**Correct answer:**

You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be .

What is the diameter of the crater?

To solve this, we need to recall the formula for the area of a circle.

Now, we know A, so we just need to plug in and solve for r!

Begin by dividing out the pi

Then, square root both sides.

Now, recall that diameter is just twice the radius.