lesson 7.2 objective: to find area and circumference of circles. center radius diameter...

Lesson 7.2

Objective: To find area and circumference of circles.

Center

Radius

Diameter

Circumference

Lesson 7.2 Area and Circumference

Circumference

You can find the circumference if you know the diameter (d) or the radius (r) of the circle.

2

C d

C r


Example

Find the circumference of a circle with a radius of 8.

2 (8)

16

50.24

C

This is the circumference “in terms of pi”.

When computing C in decimal, use 3.14 or the pi button.


Semicircle

• Half of a circle.• Its measure is 180.• Its length is one-half the circumference.


Problem 1

An indoor track at a gym has the design below. What is the length of the entire track?

100 ft

40 ft


Problem 1 Solution

The ends make one circle.

100 ft

40 ft

The diameter is 40 ft.

C = (40)


Problem 1 Solution

100 ft

40 ft

Add 200 for the straight segments.

Perimeter = 40 + 200 ft

Or, 325.66 ft.


Area of a Circle

r

2A r


Example

7 in

Find the area of the circle.

Solution:

A = (72) = 49 in2

or

A 153.94 in2


EX: Find the area of the shaded region

20 m

Find the area of the square and circle.

Subtract the area of the circle from the area of the square

Area of square 20 X 20 = 400

Area of the circle

Square – circle 400 – 314


Example

At Moldy Cheese Pizza they sell two sizes of pizza: medium and large. The medium has a diameter of 10 inches and the large has a diameter of 16 inches. On Fridays they have a special: you get one large pizza, or two medium pizzas for the same price. Which is the better deal?


Large

Radius = 8

Area = ?

8

64

Medium

Radius = 5

Area = ?

5

25


Large

Area = 64

8

Medium

Area = 25

5


Large

Area = 64

8

Medium

Area = 25

So two medium pizzas have an area

of

5 5

50


Solution: Buying one large has more area than two mediums.

8

5 5

64

25 25201 in2

157 in2


Problem

4 ftTo water a square yard, a man installs four sprinkler heads as shown. The sprinkler heads spray water in a circular pattern with a radius of 4 feet. After a while, he notices some the grass is dying. What is the area of the yard that doesn’t get any water?


Problem Solution

4 ft

?8 ft

?16 ft

?16 ft

Area of square

A = 162 = 256 ft2

Area of one circle

A = (42) = 16 ft2

Area of four circles

A = 4(16) = 64

A 201 ft2Dying Area

256 – 201 = 55 ft2


Your Turn

Find the area of the (ring) – the shaded region.

5 in 2 in


Solution

Find the area of the (ring).

5 in 2 in

Area of Outer Circle

Radius = 7 in.

Area = 49

Area of Inner Circle

Radius = 5

Area = 257

49

25


Solution

5 in 2 in

Outer Circle Area = 49

Inner Circle Area = 25

Area

Outer – Inner =

49 - 25 = 24

75.4 in2

25

49

lesson 7.2 objective: to find area and circumference of circles. center radius diameter...

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