Aim: Area of Circle Course: Applied Geo.

Do Now: Find the perimeter of an enclosed semicircle with radius of 14:

Aim: How do we find the area of a circle?

C = D = 2RC = D = 2R

R = 14, = 22/7R = 14, = 22/7

2R + ½ Circumference = perimeter 28 + 44 = 72 perimeter of semicircle

If C = R , then 1/2 C = 1/2(2R)

))()(( 1427

22

2

1

2

1C 2

= 44

Aim: Area of Circle Course: Applied Geo.

Estimating the Area of a Circle

Estimate the area of a circle with a radius of 5 using squares.

r

Area of outer square = 102 = 100 units2

Area of inner square = Area of 4 right triangles = 4(1/2)(5)(5) = 50 units2

Area of circle approximates average of twoArea of circle (100 + 50)/2 = 75 units2

Aim: Area of Circle Course: Applied Geo.

Formula for Area of Circle

A = r2

Find the Area:

r = 7

A = (7)2

A = 22/7(49)A = 154 sq. units

Find the Area:

d = 10 A = (5)2

A = 3.14(5)A = 15.7 sq. units

(radius = ½ of diameter)(radius = ½ of 10 = 5)

Aim: Area of Circle Course: Applied Geo.

Model Problem

The area of a circle is 200 sq units. Calculate the circle’s radius to the nearest hundredth.

Aim: Area of Circle Course: Applied Geo.

Model Problem

B

C

O

A

D b1 = 6

b2 = 4

h = 6r = 6

Area of Trapezoid ABCD = ½h(b1 + b2)

Find the Area of the Shaded Region

= ½(6)(6 + 4) = 30 sq. units

Area of Circle O = r2 ; r = 6

= 3.14(6)2 = 113.04

Area of shaded region = area of circle - area of trapezoid =

113.04 - 30 = 83.04 83.0 sq. units

Aim: Area of Circle Course: Applied Geo.

Model Problem

O is the center of concentric circles. Find the Area of the Shaded Region to the nearest tenth.

10 5

O

A = r2

Shaded region = Area of larger circle – area of smaller circle

Area of larger circle - A1 = 3.14(15)2

= 706.5

Area of smaller circle - A2 = 3.14(10)2 = 314

Shaded region - A1 - A2 = 706.5 - 314 =392.5 sq. units

Aim: Area of Circle Course: Applied Geo.

Model Problem

Off the coast of Sweden, divers are working to bring up artifacts from a ship that sank several hundred years ago. The line to a diver is 100 feet long, and the diver is working a a depth of 80 feet. What is the area of the circle that the diver can cover? Round to nearest square foot.

100 ft.

80 ft.

What is the radius of the circle?

c2 = a2 + b2; 1002 = 802 + b2;

b

60 ft.

b = 60

A = 3.14(60)2 = 3.14(3600) = 11,304 sq. feet

A = r2

Aim: Area of Circle Course: Applied Geo.

Model Problem

Find the area of a circle with the given radius.

r = 3 in r = 9 cm. r = 15 km

Find the area of a circle with the given diameter.

d = 24 in d = 100 cm. d = 90 km

Find the radius of a circle with the given area.

A = 210 in2 A = 1000 m2 A = 314 km2