UNIT 9

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CORNELL NOTES HEADER

Topic: Geometry 6th Grade (Unit 9 pg. 5)

E. Q.: How does the area of a circle relate to the area of a square or rectangle?

Name: _____________________________Date: _____________________________Class: _____________________________

Chp. 10 Lesson 4 –Area of a Circle

VOCABULARY REVIEW

Pi -

The ratio of a circle’s circumference to its diameter. To approximate pi, use 22/7 or 3.14. When the diameter or radius is a multiple of 7, it will be easier to use 22/7 for π.

diameter –

The distance across the circle through its center, d.

circumference –

The distance around a circle, C.

radius –

the distance from the center to any point on the circle, r.

AREA OF A CIRCLE

Formula for Area of a Circle: A = π r2

where π = pi r = radius r2 = r r

Ex. You are making a design for a circular button. Your design fits on a circle with a radius of 3 cm. How much area will be covered by your design?

3 cm

A = πr2

A = (3.14)(3)2

A = (3.14)(9)

A = 28.26 cm2

*Estimate to check: 3 x 9 = 27

AREA OF A CIRCLE EXAMPLE

Ex. Find the area of the circle.

20 cm

A = πr2

A = (3.14)(10)2 ** divide the diameter by 2 to get the radius

A = (3.14)(100)

A = 314 cm2

*Estimate to check: 3 x 100 = 300

FINDING THE AREA OF COMBINED FIGURES

Find the area of each shape in the figure and then add the areas to find the total area.

 

Ex. Find the area of the free throw area to the nearest square foot.

Arec = lw Ahalfcir = ½ π r2

A = (19)(12) A = ½ (3.14)(6)2

A = 228 ft2 A = 56.52 ft2

Estimate: 20(12) = 240 Estimate: ½(3)(36) = 54

Afreethrow = Arec + Ahalfcir

= 228 + 56.52 = 284.52 ft2 or 285 ft2

Estimate: 240 + 54 = 294

6 ft12 ft

19 ft

GROUP PROBLEM

How many times as great as the area of an 8 inch pizza is the area of a 16 inch pizza?

A8in = πr2 A16in = π r2

A = 3.14(4)2 A = 3.14(8)2

A = 50.24 in2 A = 200.96 in2

 

200.96 = 4

50.24

The area of a 16 inch pizza is four times the area of an eight inch pizza.