Transcript Ch 9-4 Circumference and Area

9-4 Circumference and Area
California
Standards
MG2.1 Use formulas routinely for finding
the perimeter and area of basic twodimensional figures and the surface area and
volume of basic three-dimensional figures,
including rectangles, parallelograms, trapezoids,
squares, triangles, circles, prisms, and cylinders.
Also covered: MG3.2
Holt CA Course 1
9-4 Circumference and Area
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.
Holt CA Course 1
9-4 Circumference and Area
Holt CA Course 1
9-4 Circumference and Area
Remember!
Pi () is an irrational number that is often
approximated by the rational numbers 3.14
and 22 .
7
Holt CA Course 1
9-4 Circumference and Area
Additional Example 1: Finding the Circumference
of a Circle
Find the circumference of each circle, both
in terms of  and to the nearest tenth. Use
3.14 for .
A. circle with a radius of 4 m
C = 2r
= 2(4)
= 8 m  25.1 m
B. circle with a diameter of 3.3 ft
C = d
=  (3.3)
= 3.3 ft  10.4 ft
Holt CA Course 1
9-4 Circumference and Area
Check It Out! Example 1
Find the circumference of each circle, both
in terms of  and to the nearest tenth. Use
3.14 for .
A. circle with a radius of 8 cm
C = 2r
= 2(8)
= 16 cm  50.2 cm
B. circle with a diameter of 4.25 in.
C = d
= (4.25)
= 4.25 in.  13.3 in.
Holt CA Course 1
9-4 Circumference and Area
Holt CA Course 1
9-4 Circumference and Area
Additional Example 2: Finding the Area of a Circle
Find the area of each circle, both in terms of 
and to the nearest tenth. Use 3.14 for .
A. circle with a radius of 4 in.
A = r2 = (42)
= 16 in2  50.2 in2
B. circle with a diameter of 3.3 m
d
= 1.65
2
= 2.7225 m2  8.5 m2
A = r2 = (1.652)
Holt CA Course 1
9-4 Circumference and Area
Check It Out! Example 2
Find the area of each circle, both in terms of 
and to the nearest tenth. Use 3.14 for .
A. circle with a radius of 8 cm
A = r2 =  (82)
= 64 cm2  201.0 cm2
B. circle with a diameter of 2.2 ft
d
2
2
A = r =  (1.1 )
2 = 1.1
= 1.21 ft2  3.8 ft2
Holt CA Course 1
9-4 Circumference and Area
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  and to the nearest tenth. Use
3.14 for .
A = r2
Holt CA Course 1
C = d
= (32)
= (6)
= 9 units2
= 6 units
 28.3 units2
 18.8 units
9-4 Circumference and Area
Check It Out! Example 3
Graph the circle with center (–2, 1) that passes
through (–2, 5). Find the area and circumference,
both in terms of  and to the nearest tenth. Use
3.14 for .
y
A = r2
(–2, 5)
= (42)
= 16 units2
4
x
(–2, 1)
Holt CA Course 1
 50.2 units2
C = d
= (8)
= 8 units
 25.1 units
9-4 Circumference and Area
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 .
C = d = (56)
 22 (56) 
7
Find the circumference.
22 56  176 ft
7 1
The distance is the circumference of the
wheel times the number of revolutions, or
about 176  15 = 2640 ft.
Holt CA Course 1
9-4 Circumference and Area
Check It Out! 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 .
C = d =  (14)
 22 (14) 
7
12
9
3
6
Holt CA Course 1
Find the circumference.
22 14
7 1
 44 in.
The distance is the circumference of the
clock times the number of revolutions,
or about 44  60 = 2640 in.