1. This document outlines objectives and concepts for calculating arc length and sector area of circles, as well as solving apparent size problems. It includes formulas for finding arc length and sector area given the radius and central angle in both degrees and radians. It also provides example problems to solve for radius, central angle, arc length, and sector area using given information. 2. Apparent size depends on both an object's actual size and the angle it subtends from the observer's perspective. Examples demonstrate using apparent size and distance to calculate approximate diameters of Jupiter and Mars.

1. Objectives
1. Find arc length of a circle
2. Find area of a sector
3. Solve apparent size problems

2. A
sector of a circle is the region
bounded by a central angle and the
intercepted arc.
 The arc length is some fraction of
the circumference.
 The sector area is the same fraction
of the circle’s area.

3. θ
= 60 and r = 12
 Arc length = s =
circumference
or
 Sector
Area = K =
of the

4.  For
 In
θ in degrees:
radians:

5. A
sector of a circle has arc length 6
cm and area 75cm2. Find its radius
and central angle measure.

6. A
sector has perimeter 16 cm and
area 15 cm2. Find its radius r and arc
length s.

7. = 6 and θ = 2π/3
 Find the arc length and sector area.
r

8.  How
big a far away object looks
depends on its size and also the
angle that it subtends at our eyes.
 This angle is the object’s apparent
size.

9.  Jupiter
has an apparent size of 0.01
when it is 8x108 km from Earth. Find
the approximate diameter of Jupiter.

10.  At
its closest approach, Mars is about
5.6 x 107 km from Earth and its
apparent size is about 0.00012
radians. What is the approximate
diameter of Mars?