Transcript 7.2 Sectors of Circles

7.2 Sectors of Circles
To find arc length and area of a sector
of a circle
To solve problems involving apparent
size
Formulas
• Sector of a circle
(Area):
• Arc Length:
Degrees:
Degrees:
Radians
Radians
Arc Length/Area
• A sector of a circle has an arc length of
6cm and area of 75 cm2 Find its radius
and the measure of its central angle.
Arc Length/Area
• A sector of a circle has a radius of 5cm
and a central angle of 3 radians. Find its
arc length and area.
Find the arc length and area.
• R =4,
• R=6,
 = 45o

2
=
3
Sectors
1. A sector has a perimeter of 16 cm and area of 15 cm . Find the radius and the
arc length.
2
2. A sector has a central angle of 24 and an arc length of 8.4 cm . Find the
area to the nearest square centimeter.

3. A sector has an area of 100 cm and a central angle of .5 radians. Find the
radius and the arc length.
2
Apparent Size
• When there is nothing on our field of vision against which to judge the
size of an object, we perceive the object to be smaller when it is
farther away. For example, the sun is much larger than the moon, but
we perceive the sun to be about the same size as the moon because
the sun is so much farther from Earth. Thus, how big an object looks
depends not only on its size but also on the angle that it subtends at
our eyes. The measure of this angle is called the object’s apparent
size.
Apparent Size
• The apparent size of a tall building 2km
away is .05 radians. What is the buildings
approximate height?
Apparent Size
•
The diameter of the moon is about 3500
km. Its apparent size is about 0.0087
radians. What is the approximate
distance from the Earth?
Apparent Size
•
You are travelling in a car toward a
certain mountain known to be 25m high.
The apparent size of the mountain is
0.55. Twenty minutes later the same
mountain has an apparent size of 1.3.
What is the approximate speed of the car
in Km/h?
Application
• A phonograph record with a diameter of 12
inches turns @ 33 1/3 rpm. Find the
distance that a point on the rim travels in 1
minute.
Homework:
• P. 264. 1-10all, 12-15,20.