Intro to Circles

Intro to Circles

What is a circle?

• A circle is the set of all points in a plane that are a given distance, the radius, from a given point, the center.

Parts of a Circle

• A diameter is a segment that contains the center of a circle and has both endpoints on the circle.

• A radius is a segment that has one endpoint at the center of the circle and the other endpoint on the circle.

• A central angle is an angle whose vertex is the center of the circle.

What is pi?

• Pi, represented by the symbol,  $\pi$  , is the ratio of the circumference to the diameter of a circle.

• That means that pi is the number of diameters needed to form the circumference of a circle.

• It is a number that is a little more than 3. 

• Since  $\pi$  =  $\frac{c}{d}$  , we can find the circumference by solving for c. 

• c =  $\pi d$  or c =  $2\pi r$  

In terms of pi

• In our study, you will often be asked to leave your answer in terms of  $\pi$  .  That means  $\pi$  will be in the final answer.  In short, do not enter  $\pi$  in your calculator.  When you do, your calculator uses an approximation for pi (since it's irrational).  Leaving your answer in terms of pi means it is an EXACT answer. 

Area of a circle

• In the diagram to the right, the circle is at the top is divided into smaller parts called sectors. These sectors are put together in such a way as to form a parallelogram. 

Area of a Circle

• The area of a parallelogram is found by multiplying the base times the height. The base is half of the circumference. So half of  $2\pi r$  is  $\pi r$ .  The height of the parallelogram is the radius of the circle. Hence, the area of the circle is bh, which is  $\pi r$  times  $r$  , giving us  $A\ =\ \pi r^2$   

Multiple Choice

The perimeter of a circle is usually called the...

• radius

• diameter

• circumference

• area

Multiple Choice

The distance across the circle through the center is called the...

• radius
• diameter
• circumference
• area

Multiple Choice

The distance from the center of the circle to any point on the circle is called the...

• radius
• diameter
• circumference
• area

Multiple Choice

A central angle has its vertex...

• ...on the circle
• ...outside the circle
• ...on one of the three sides of the circle
• ...on the center of the circle

Multiple Choice

If you multiply  $\pi\ \cdot r^2$   then you will get the...

• Circumference

• Area

• Radius

• Diameter

Multiple Choice

Does this picture show the diameter or radius of a circle?

• Diameter
• Radius

Multiple Choice

What is the diameter of this circle?

• 8 cm

• 16 cm

• 10 cm

• 4 cm

Multiple Choice

What is the radius of this circle?

• 18 ft

• 72 ft

• 38 ft

• 14 ft

Multiple Choice

Does this picture show the diameter or radius of a circle?

• Diameter

• Radius

Multiple Choice

If you multiply  $\pi\cdot d$   then you will get the...

• radius

• diameter

• circumference

• area

Multiple Choice

What is the circumference of this circle?

• 3.14 cm 
• 37.7 cm
• 24 cm
• 68.4 cm

Multiple Choice

If you multiply  $2\cdot r$   then you will get the...

• radius

• diameter

• circumference

• area

Multiple Choice

If a circle has a diameter of 10 feet, then which statement is true?

• The radius is 5 ft.

• The diameter is 5 ft

• The radius is 20 ft.

• The diameter is 20 ft.

Multiple Choice

If a circle has a radius of 10 feet, then which statement is true?

• The radius is 5 ft.

• The diameter is 5 ft

• The radius is 20 ft.

• The diameter is 20 ft.

Multiple Choice

Which segment is a radius?

• $\overline{LM}$

• $\overline{DC}$
  

• $\overline{BD}$
  

• $\overline{ML}$
  

Multiple Choice

Which segment is the diameter?

• $\overline{AC}$

• $\overline{BD}$
  

• $\overline{LM}$
  

• $\overline{CE}$
  

Multiple Choice

What is the area of this circle?
d = 8cm

• 16π
• 8π
• 4π
• 36π

Multiple Choice

Which answer is in terms of pi?

• 
  

  $14\pi$

• 3.14

• 9 * 3.14

• 18.32

Multiple Choice

Which answer is rounded to the nearest hundreth?

• $14\pi$

• 3.1456

• 9 * 3.14

• 18.32