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 8in.

We also know that.

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

You want to ice skate around the outer edge of a circular pond (the water is frozen, because it is January and you live in Wisconsin). If the pond has a radius of 35 meters, how far will you skate in one lap around the pond?

Let's begin by realizing what we are being asked for. They want us to find the total distance we will travel in one lap around the pond. This sounds like circumference, because we are going one full distance around the outside of the circle.

The formula for circumference is as follows.

Now, we have r, so just plug in and solve.

So, our answer is:

You are conducting fieldwork, when you find a tree whose radius at chest height is . What is the circumference of the tree at chest height?

The formula for circumference of a circle is:

We have r, so simply plug it in and solve:

So, our answer is 

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

where d is the diameter of the circle.

Now, we know the diameter of the circle is 18cm.  So, we will substitute.  We get

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 10in.  

So, we get

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 circumference 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.

Next, plug our answer into the circumference formula.

Sector TYP occupies 43% of a circle. Find the degree measure of angle TYP.

Use the following formula and solve for x:

Begin by dividing over the 100

Then multiply by 360

If sector AJL covers 45% of circle J, what is the measure of sector AJL's central angle?

To find an angle measure from a percentage, simply convert the percentage to a decimal and then multiply it by 360 degrees.

So, our answer is 162 degrees.

If we let  be the circumference of the circle, then the length of  is  of the circumference, so

The radius is the circumference divided by :

Use the formula to find the area of the entire circle:

The area of the white region is  of that of the circle, or 

The radius of a circle is found by dividing the circumference  by :

The area of the entire circle can be found by substituting for  in the formula:

.

The area of the shaded  sector is  of the total area: