Transcript Circumference and Areas of Circles

Circumference and Areas of
Circles
Lesson 11.5
Geometry Honors
Objective: Know and use the
formulas for the Circumference
and Areas of Circles
Lesson Focus
In this lesson, the formulas for circumference and area of a
circle are stated. These formulas can be understood by using
facts that have been developed about areas of regular
polygons.
Summary
Basic Terms
Circumference
The perimeter of or distance around a circle.
Area of a Circle
The area of a disk (the region inside a circle) is πr2 when the
circle has radius r.
π
An irrational number that is the ratio of the circumference of
a circle to its diameter.
Area of a Circle
Area, A = πr2
Circumference
Circumference, C = 2πr = πd
Pi
• Leave answers in π form
unless an approximation is
specified.
• The exact circumference or
exact area of a circle requires
that π be approximated.
• π is an irrational number is
not the ration of two integers, as
the quotient 22/7 suggests.
• In the expression C/d, d is
rational, C is not, and vice
versa.
Practice
1. What is the ratio of the circumference to the diameter for
each circle?
2. A circle has a radius of 15. What is the diameter,
circumference, and area of the circle?
3. A circle has a diameter of 8. What is the radius,
circumference, and area of the circle?
4. A circle has a circumference of 26π. What is the radius,
diameter, and area of the circle?
5. A circle has an area of 100π. What is the radius, diameter,
and circumference of the circle?
Written Exercises
Problem Set 11.5, p.448: # 2 – 16 (even)
Handout: 11-5