8.5 Areas of - Mount Horeb Middle School · PDF fileGeometry Agenda: 8.5 Areas of 2 February...
Transcript of 8.5 Areas of - Mount Horeb Middle School · PDF fileGeometry Agenda: 8.5 Areas of 2 February...
8.5 Areas of Circles.notebook
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• 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:
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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
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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
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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
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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?
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Review Problems from book problems 8.5
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11. 12.
13. 14.
Let's set up 1114 together.
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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.**
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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
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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?
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Lesson 8.5 Book Problems Name___________________
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11. 12.
13. 14.
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Assingment: Lesson 8.5 p.451 #114,17,18
This is on the back of your note sheet.
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