Circumference
Circumference is the distance around a circle. The circumference can also be called the perimeter of a circle. However, we use the term circumference for circles because they are round.
Circumference Formula:
You should have a
What if you were given the radius or diameter of a circle? How could you find the distance around that circle?
Examples
Example 1
Find the circumference of a circle with a radius of 7 cm.
Plug the radius into the formula.
Example 2
The circumference of a circle is
Again, you can plug in what you know into the circumference formula and solve for
Example 3
A circle is inscribed in a square with 10 in. sides. What is the circumference of the circle? Leave your answer in terms of
From the picture, we can see that the diameter of the circle is equal to the length of a side.
Example 4
Find the perimeter of the square in Example 3. Is it more or less than the circumference of the circle? Why?
The perimeter is
Example 5
The tires on a compact car are 18 inches in diameter. How far does the car travel after the tires turn once? How far does the car travel after 2500 rotations of the tires?
One turn of the tire is the circumference. This would be
Review
Fill in the following table. Leave all answers in terms of
diameter | radius | circumference | |
---|---|---|---|
1. | 15 | ||
2. | 4 | ||
3. | 6 | ||
4. | |||
5. | 9 | ||
6. | |||
7. | |||
8. | 36 |
- Find the circumference of a circle with
d=20π cm .
Square
- Find the length of the diameter of
⨀T . - How does the diameter relate to
PQSR ? - Find the perimeter of
PQSR . - Find the circumference of
⨀T .
For questions 14-17, a truck has tires with a 26 in diameter.
- How far does the truck travel every time a tire turns exactly once? What is this the same as?
- How many times will the tire turn after the truck travels 1 mile? (1 mile = 5280 feet)
- The truck has travelled 4072 tire rotations. How many miles is this?
- The average recommendation for the life of a tire is 30,000 miles. How many rotations is this?
Review (Answers)
To see the Review answers, open this PDF file and look for section 10.8.