Notes: Converting to radian and circumference and area of a circle

Converting: degrees to radians radians to degrees

360 360 2K

Circumference = 2nr or Tid

Area = Tcr

ex.1. Convert 45° to radians ex.2 Convert Y to degrees

"Exact" and "leave in terms of n" - do not multiple by 3.14 or any other value for n.

Answers will be left with "TU" symbol

Find the circumference and area of each circle:

exact value ex. 1 r=5. C'^ff^

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ex.2 d=7 C rfJ

c= IOTT

A-'HIT

P'itimate . .

ex. 3 Find the are^ of the circle with circumference 227i. Leave answer in terms of TT

err trr y> - - - ^ r / ^ i T f ^ ex. 4 A radio tower has a transmission of 100 km. How much of the city's a^g^will it cover? Leave answer in terms of n and then estimate the area to the nearest tenth of a kilometer.

^ 1 V/r.^^A-ex.5 If a bicycle tire has a diameter of 20 in, howlar wiTi Sarah ride in 12j;eyolutions? Estimate the distance she traveled to the nearest lenth of an inch, i i, ^ zJi2o-iT \

Notes on Circles: Arc Length, Area of Sector, and Segment.

*Remember: Circumference= 27ir or 7id Area = 7ir

Ex: Find the circumference and the area

C= 2rrr = 2tT7 = l^-rft

The length of an arc is a fraction of the circumference of the circle.

T E R M D I A G R A M LENGTH

Arc length is the distance along an arc measured in

A

0. 2. Find e a c h arc length . Give your answer in terms o f 71 and r o u n d e d Lo die neaiesL h u n d i e d l h .

36. o

Area of a section is a fraction of the area of the circle Sttctor off a Circio

T E R M N A M E D I A G R A M A R E A

A sector of a circle is a region bounded by two radii of the circle and their intercepted arc.

sector ACB

A

(^ e J'!,xamples: Innd the area of each sector. Give answers in terms of TT.

4.

r

3.

.it

0^ m.

A segment of a circle is a region bounded by an arc and its chord. Area off a Sogmont

0 = (3 area of segment = area of sector - area of triangle

5. Find the area of each to the nearest hundredth.

-. n it rr