Transcript circle

6-4
Circles
Warm Up
Problem of the Day
Lesson Presentation
Course 3
6-4 Circles
Warm Up
1. Find the length of the hypotenuse of a right
triangle that has legs 3 in. and 4 in. long.
5 in.
2. The hypotenuse of a right triangle measures 17
in., and one leg measures 8 in. How long is the
other leg?
15 in.
3. To the nearest centimeter, what is the height of
an equilateral triangle with sides 9 cm long?
8 cm
Course 3
6-4 Circles
Problem of the Day
A rectangular box is 3 ft. by 4 ft. by 12 ft.
What is the distance from a top corner to
the opposite bottom corner?
13 ft
Course 3
6-4 Circles
Learn to find the area and circumference
of circles.
Course 3
6-4 Circles
Vocabulary
circle
radius
diameter
circumference
Course 3
6-4 Circles
A circle is the set of points in a plane
that are a fixed distance from a given
point, called the center. A radius
connects the center to any point on the
circle, and a diameter connects two
points on the circle and passes through
the center.
Course 3
6-4 Circles
Radius
Center
Diameter The diameter d is
twice the radius r.
d = 2r
Circumference
The circumference of a circle is the distance
around the circle.
Course 3
6-4 Circles
Course 3
6-4 Circles
Remember!
Pi (p) is an irrational number that is often
approximated by the rational numbers 3.14
and 22 .
7
Course 3
6-4 Circles
Additional Example 1: Finding the Circumference of a
Circle
Find the circumference of each circle, both
in terms of p and to the nearest tenth. Use
3.14 for p.
A. Circle with a radius of 4 m
C = 2pr
= 2p(4)
= 8p m  25.1 m
B. Circle with a diameter of 3.3 ft
C = pd
= p(3.3)
= 3.3p ft  10.4 ft
Course 3
6-4 Circles
Try This: Example 1
Find the circumference of each circle, both
in terms of p and to the nearest tenth. Use
3.14 for p.
A. Circle with a radius of 8 cm
C = 2pr
= 2p(8)
= 16p cm  50.2 cm
B. Circle with a diameter of 4.25 in.
C = pd
= p(4.25)
= 4.25p in.  13.3 in.
Course 3
6-4 Circles
Course 3
6-4 Circles
Additional Example 2: Finding the Area of a Circle
Find the area of each circle, both in terms of p
and to the nearest tenth. Use 3.14 for p.
A. Circle with a radius of 4 in.
A = pr2 = p(42)
= 16p in2  50.2 in2
B. Circle with a diameter of 3.3 m
A = pr2 = p(1.652)
= 2.7225p m2  8.5 m2
Course 3
d
= 1.65
2
6-4 Circles
Try This: Example 2
Find the area of each circle, both in terms of p
and to the nearest tenth. Use 3.14 for p.
A. Circle with a radius of 8 cm
A = pr2 = p(82)
= 64p cm2  201.0 cm2
B. Circle with a diameter of 2.2 ft
A = pr2 = p(1.12)
= 1.21p ft2  3.8 m2
Course 3
d
2
= 1.1
6-4 Circles
Additional Example 3: Finding the Area and
Circumference on a Coordinate Plane
Graph the circle with center (–2, 1) that passes
through (1, 1). Find the area and circumference,
both in terms of p and to the nearest tenth. Use
3.14 for p.
A = pr2
Course 3
C = pd
= p(32)
= p(6)
= 9p units2
= 6p units
 28.3 units2
 18.8 units
6-4 Circles
Try This: Example 3
Graph the circle with center (–2, 1) that passes
through (–2, 5). Find the area and circumference,
both in terms of p and to the nearest tenth. Use
3.14 for p.
y
A = pr2
(–2, 5)
4
x
(–2, 1)
Course 3
= p(42)
= 16p units2
 50.2 units2
C = pd
= p(8)
= 8p units
 25.1 units
6-4 Circles
Additional Example 4: Measurement Application
A Ferris wheel has a diameter of 56 feet
and makes 15 revolutions per ride. How far
would someone travel during a ride? Use 22
7
for p.
C = pd = p(56)
Find the circumference.
22 56
22
 176 ft

(56)

7
7
1
The distance is the circumference of the
wheel times the number of revolutions, or
about 176  15 = 2640 ft.
Course 3
6-4 Circles
Try This: Example 4
A second hand on a clock is 7 in long. What
is the distance it travels in one hour? Use 22
7
for p.
C = pd = p(14)
22 14
22

(14)  7
7
1
12
9
3
6
Course 3
Find the circumference.
 44 in.
The distance is the circumference of the
clock times the number of revolutions, or
about 44  60 = 2640 in.
6-4 Circles
Lesson Quiz
Find the circumference of each circle, both
in terms of p and to the nearest tenth. Use
3.14 for p.
1. radius 5.6 m
11.2p m; 35.2 m
2. diameter 113 m 113p mm; 354.8 mm
Find the area of each circle, both in terms of
p and to the nearest tenth. Use 3.14 for p.
3. radius 3 in.
9p in2; 28.3 in2
4. diameter 1 ft
0.25p ft2; 0.8 ft2
Course 3