View
214
Download
1
Category
Preview:
Citation preview
8.5 Areas of Circles.notebook
1
February 13, 2014
• Return Quiz 8.18.2 • Correct 8.3 Worksheet• Lesson 8.5 Notes Area of a circle formula.• You will need your calculator for these notes.
Geometry Agenda:
8.5 Areas of Circles.notebook
2
February 13, 2014
8.3 WS key 1. a) 121,952 ft2 b) 244 gallons primer and 488 gallons finishing paint.
2. 4 rolls, 3.84 rolls to cover 480 ft2
3. a) 219.5 ft2, b) 16 bundles; $638.40
4. 350 liters
5. cut in half
6. 100 square units
8.5 Areas of Circles.notebook
3
February 13, 2014
8.5 Areas of Circles.notebook
4
February 13, 2014
8.5 Areas of Circles.notebook
5
February 13, 2014
8.5 Areas of Circles.notebook
6
February 13, 2014
8.5 Areas of Circles.notebook
7
February 13, 2014
8.5 Areas of Circles.notebook
8
February 13, 2014
8.5 Areas of Circles.notebook
9
February 13, 2014
8.5 Areas of Circles.notebook
10
February 13, 2014
8.5 Areas of Circles.notebook
11
February 13, 2014
Lesson 8.5 Area of CirclesIf we divide a circle into equal wedges and arrange them in a row alternating their direction we will see that the shape that they form is a parallelogram.
Since we know that the distance around the circle is C = 2 πr, we know the base of this parallelogram will be _______ and the height will be h ≈ ________.
And if we kept dividing these wedges ininitely we would end up with a rectangle with a base and height exactly equal to these.
So the formula for inding the area of any circle is:
Area of a circle = πr2
8.5 Areas of Circles.notebook
12
February 13, 2014
When balancing equations, to get a variable alone that is raised to the second power, we need to take the square root of both sides of the equation.
x2 = 9 2r2 = 50
πr2 = 15ππr2 = 49
2
8.5 Areas of Circles.notebook
13
February 13, 2014
Ex 5. Find the cicumference of a circle that has an area of 256 π ft2.
Ex 2. If A = 5π in.2, then r = ?.Ex 1. If r = 8 cm, then A = ?.
Ex 3. If A = 16π in.2, then r = ?. Ex 4. If C = 216in., then A ≈ ?.
Examples of using the area of a circle formula
x
y
(4, 7)
(8, 0)
(6, 5)
Ex 6. What is the area of the shaded region between the circle and the trapezoid?
8.5 Areas of Circles.notebook
14
February 13, 2014
Review Problems from book problems 8.5
8.5 Areas of Circles.notebook
15
February 13, 2014
11. 12.
13. 14.
Let's set up 1114 together.
8.5 Areas of Circles.notebook
16
February 13, 2014
8.5 Areas of Circles.notebook
17
February 13, 2014
8.5 Areas of Circles.notebook
18
February 13, 2014
8.5 Areas of Circles.notebook
19
February 13, 2014
8.5 Areas of Circles.notebook
20
February 13, 2014
Exiting problems using the area of a circle formula
1. If r = 9 cm, then A = ?. 2. If A = 7π in.2, then r = ?.
3. Find the cicumference of a circle that has an area of 144 π ft2.
c. A = 81π cmb. A = 9π cma. A = 18π cm
c. r = 2.5 in.
a. r = √7 in.π
b. r = √7 in.
b. C = 24π ft2
a. C = 12π ft2
c. C = 144π ft2
**Remember to put your name on a small slip of paper and copy your multiple choice answers onto it an put it in the basket.**
8.5 Areas of Circles.notebook
21
February 13, 2014
Lesson 8.5 Area of CirclesThe formula for inding the area of any circle is:
When balancing equations, to get a variable alone that is raised to the second power, we need to take the square root of both sides of the equation.
x2 = 9 2r2 = 50
πr2 = 15ππr2 = 49
Ex 5. Find the cicumference of a circle that has an area of 256 π ft2.
Ex 2. If A = 5π in.2, then r = ?.Ex 1. If r = 8 cm, then A = ?.
Ex 3. If A = 16π in.2, then r = ?. Ex 4. If C = 216in., then A ≈ ?.
Examples of using the area of a circle formula
Area of a circle = πr2
1
Review Problems from book problems 8.5
x
y
(4, 7)
(8, 0)
(6, 5)
Ex 6. What is the area of the shaded region between the circle and the trapezoid?
8.5 Areas of Circles.notebook
22
February 13, 2014
Lesson 8.5 Book Problems Name___________________
1
11. 12.
13. 14.
8.5 Areas of Circles.notebook
23
February 13, 2014
Assingment: Lesson 8.5 p.451 #114,17,18
This is on the back of your note sheet.
8.5 Areas of Circles.notebook
24
February 13, 2014
Recommended