lesson 7.2 objective: to find area and circumference of circles. center radius diameter...
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Lesson 7.2
Objective: To find area and circumference of circles.
Center
Radius
Diameter
Circumference
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Lesson 7.2 Area and Circumference
Circumference
You can find the circumference if you know the diameter (d) or the radius (r) of the circle.
2
C d
C r
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Lesson 7.2 Area and Circumference
Example
Find the circumference of a circle with a radius of 8.
2 (8)
16
50.24
C
This is the circumference “in terms of pi”.
When computing C in decimal, use 3.14 or the pi button.
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Lesson 7.2 Area and Circumference
Semicircle
• Half of a circle.• Its measure is 180.• Its length is one-half the circumference.
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Lesson 7.2 Area and Circumference
Problem 1
An indoor track at a gym has the design below. What is the length of the entire track?
100 ft
40 ft
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Lesson 7.2 Area and Circumference
Problem 1 Solution
The ends make one circle.
100 ft
40 ft
The diameter is 40 ft.
C = (40)
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Lesson 7.2 Area and Circumference
Problem 1 Solution
100 ft
40 ft
Add 200 for the straight segments.
Perimeter = 40 + 200 ft
Or, 325.66 ft.
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Lesson 7.2 Area and Circumference
Area of a Circle
r
2A r
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Lesson 7.2 Area and Circumference
Example
7 in
Find the area of the circle.
Solution:
A = (72) = 49 in2
or
A 153.94 in2
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Lesson 7.2 Area and Circumference
EX: Find the area of the shaded region
20 m
Find the area of the square and circle.
Subtract the area of the circle from the area of the square
Area of square 20 X 20 = 400
Area of the circle
Square – circle 400 – 314
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Lesson 7.2 Area and Circumference
Example
At Moldy Cheese Pizza they sell two sizes of pizza: medium and large. The medium has a diameter of 10 inches and the large has a diameter of 16 inches. On Fridays they have a special: you get one large pizza, or two medium pizzas for the same price. Which is the better deal?
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Lesson 7.2 Area and Circumference
Large
Radius = 8
Area = ?
8
64
Medium
Radius = 5
Area = ?
5
25
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Lesson 7.2 Area and Circumference
Large
Area = 64
8
Medium
Area = 25
5
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Lesson 7.2 Area and Circumference
Large
Area = 64
8
Medium
Area = 25
So two medium pizzas have an area
of
5 5
50
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Lesson 7.2 Area and Circumference
Solution: Buying one large has more area than two mediums.
8
5 5
64
25 25201 in2
157 in2
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Lesson 7.2 Area and Circumference
Problem
4 ftTo water a square yard, a man installs four sprinkler heads as shown. The sprinkler heads spray water in a circular pattern with a radius of 4 feet. After a while, he notices some the grass is dying. What is the area of the yard that doesn’t get any water?
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Lesson 7.2 Area and Circumference
Problem Solution
4 ft
?8 ft
?16 ft
?16 ft
Area of square
A = 162 = 256 ft2
Area of one circle
A = (42) = 16 ft2
Area of four circles
A = 4(16) = 64
A 201 ft2Dying Area
256 – 201 = 55 ft2
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Lesson 7.2 Area and Circumference
Your Turn
Find the area of the (ring) – the shaded region.
5 in 2 in
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Lesson 7.2 Area and Circumference
Solution
Find the area of the (ring).
5 in 2 in
Area of Outer Circle
Radius = 7 in.
Area = 49
Area of Inner Circle
Radius = 5
Area = 257
49
25
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Lesson 7.2 Area and Circumference
Solution
5 in 2 in
Outer Circle Area = 49
Inner Circle Area = 25
Area
Outer – Inner =
49 - 25 = 24
75.4 in2
25
49