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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

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?

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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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