How does the area of a circle relate to the area of a rectangle?

#### Watch This

http://www.youtube.com/watch?v=SIKkWLqt2mQ James Sousa: Determine the Area of a Circle

http://www.youtube.com/watch?v=sHtsnC2Mgnk James Sousa: Determine the Circumference of a Circle

#### Guidance

A circle is the set of all points equidistant from a center point. From the center point to the circle is called the **radius** **diameter**

The perimeter of a circle is called its **circumference**. The ratio between the circumference and diameter of any circle is

The area of a circle is also related to

**Example A**

Find the area and circumference of a circle with radius 5 inches.

**Solution:**

Leaving your answer with a

**Example B**

Find the area and circumference of a circle with diameter 16 cm.

**Solution:** If the diameter is 16 cm, then the radius is 8 cm.

**Example C**

The shape below is a portion of a circle called a sector. This sector is

**Solution:** Since the sector is

The perimeter of the sector is the sum of the lengths of the two radiuses and the arc. Each radius is 4 *in*. The arc is

**Concept Problem Revisited**

You can understand the formula for the area of a circle by dissecting a circle into wedges and rearranging them to form a shape that is close to a parallelogram. The parallelogram can then by formed into a shape close to a rectangle.

The lengths of the sides of the “parallelogram” are

#### Vocabulary

A ** circle** is the set of all points equidistant from a center point.

** Equidistant** means the same distance away from.

** Circumference** is the perimeter of a circle.

The ** radius** of a circle is the distance from the center point to the circle.

The ** diameter** of a circle is the distance from one side of the circle to the other while passing through the center point.

#### Guided Practice

1. Explain why the formula

2. Find the area of a circle with a circumference of

3. Find the area and circumference of the sector below. The sector is

**Answers:**

1. The relationship between the radius and the diameter is

2. If the circumference is

3.

#### Practice

1. Find the area and circumference of a circle with radius 3 *in*.

2. Find the area and circumference of a circle with radius 6 *in*.

3. Find the area and circumference of a circle with diameter 15 *cm*.

4. Find the area and circumference of a circle with diameter 22 *in*.

5. Find the area of a circle with a circumference of

6. Find the circumference of a circle with area

7. The sector below is

8. Find the perimeter of the sector in #7.

9. The sector below is

10. Find the perimeter of the sector in #9.

11. The sector below is \begin{align*}\frac{1}{8}\end{align*} of a circle. Find the area of the sector.

12. Find the perimeter of the sector in #11.

13. The sector below is \begin{align*}\frac{2}{3}\end{align*} of a circle. Find the area of the sector.

14. Find the perimeter of the sector in #13.

15. Explain the formula \begin{align*}A=\frac{Cr}{2}\end{align*} where \begin{align*}A\end{align*} is the area of a circle, \begin{align*}C\end{align*} is the circumference of the circle, and \begin{align*}r\end{align*} is the radius of the circle.