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Let’s look at some theorems.
10-11 Area of a Circle
The area of a circle is the product of π and
the square of the radius.
O
r A = π r ²
Example:
How much more pizza is in a 12-in-diameter pizza than in a 10-in. pizza?
r = 5
A = π(5)2
A = 25π
A = 36π – 25πA = 34.5 in2 more
r = 6
A = π(6)2
A = 36π
Here come more theorems.
10-12 AREA OF A SECTOR
THE AREA OF A SECTOR IS THE PRODUCT OF THE RATIO MEASURE OF THE
ARC AND THE AREA OF THE CIRCLE360
r
R
SO
A = m RS
360(πr²)
(
Example:Find the area of the sector of
the slice of pizza.
720
20 cm
A = m RS
360(πr²)
(
R
S
A = m 72
360(π20²)
(
A = 80π cm²A = 251.33 cm²
Here comes a term.Segment of a Circle
A part of a circle bounded by an arc and the segment joining its
endpoints.
Areaof sector – Areaof triangle = Areaof segment
R
SO
segment of a circle
EXAMPLE: Find the area of the shaded segment.
R
SO 10 in
A = m RS
360(πr²)
(
A = m 90
360(π10²)
(
A = 1/4 (100)πA = 25 π
A = 1/2 bhA = 1/2(10)(10)A = 1/2(100)A = 50
A = 25 π – 50 A = 28.53 in2