11.5 – Areas of Circles and Sectors

Area of a Circle:

A= r2

Area of a Sector: Area between two radii in a circle

2

area of sector degree of arc

360r

1. Find the area of the circle.

A= r2

A= (7)2

A= 49cm2

1. Find the area of the circle.

A= r2

A= (6.5)2

A= 42.25in2

( )

2. Find the area of the shaded figure.

A = +

A = r2

2+ bh

A = (2)2

2+ (4)(4)

44

4

A = 4 2

+ 16

A = 2 + 16 ft2

( )

2. Find the area of the shaded figure.

A = –

8in

4in

r2A = –s2

(4)2A = –(8)2

16A = –64

16A = – 64 in2

8in

3. The area of a circle is 58 square inches. Find the diameter. Round to two decimal places.

A = r2

58 = r2

18.46 = r2

4.30in = r

d = 8.59in

4. Find the area of sector formed by ACB. Round to two decimal places. Leave answers in terms of pi.

2(10)

x

360x = 6000

216.67x in

2

area of sector degree of arc

360r

60

360

220

x

360x = 40000

x = 11.11m2

2

area of sector degree of arc

360r

100

360

5. Find the area of sector formed by PSQ. Round to two decimal places. Leave answers in terms of pi.

6. Find the area of sector formed by ACB. Round to two decimal places. Leave answers in terms of pi.

110

360

360x = 7040

219.56x in

110°

2

area of sector degree of arc

360r

2(8)

x

2(5)

x

360x = 7050

282°

2

area of sector degree of arc

360r

282

360

219.58x ft

7. Find the area of sector formed by PSQ. Round to two decimal places. Leave answers in terms of pi.