Section 7-7 Circles and Sectors SPI 32L: determine the area of indicated regions involving circles SPI 33B: find the area of a sector of a circle given a diagram Objectives: Find the areas of circles, sectors, and segments of circles Recall Area of a Circle A =  r 2

Real-world and Pizza How much more pizza is in a 12 inch diameter pizza than in a 10 inch diameter pizza? 10-inch pizza Radius = 10/2 = 5 Area =  (5) 2 = 25  12-inch pizza Radius = 12/2 = 6 Area =  (6) 2 = 36  Difference in Area = 36  - 25  = 11   34.6 in 2

Sectors of Circles Sector of a Circle: region bounded by an arc of the circle and the two radii to the arcs endpoints name by using one arc endpoint, the center of the circle, and the other arc endpoint arc radius A B O (AOB of Circle O)

Area and Sectors of Circles The area of a sector is a fractional part of the area of a circle. The ratio of a sector’s area to a circle’s area is: measure of the arc 360

.. The area of sector ACB is 10 m 2. = 10 = = (6) Find the area of sector ACB. Leave your answer in terms of π. area of sector ACB = r 2 mAB 360 Areas of Circles and Sectors

Segments of a Circle Part of the circle bounded by an arc and the segments joining the arc’s endpoints Segment of a circle

Finding Area of a Segment of a Circle ? = - = -

= (24) 2 Substitute = 576 = 192 Simplify area of sector AOB = r 2 Use the formula for area of a sector. mAB 360 Areas of Circles and Sectors Find the area of the shaded segment. Round your answer to the nearest tenth. Step 1: Find the area of sector AOB.

A = bhArea of a triangle A = (24 3 )(12)Substitute 24 for b and 12 for h. A = 144 3Simplify You can use a 30°-60°-90° triangle to find the height h of AOB and AB. 24 = 2hhypotenuse = 2 shorter leg 12 = hDivide each side by 2. = 3 12 = 12 3longer leg = 3 shorter leg AB = 24 3Multiply each side by 2. AB 2 (continued) Step 2: Find the area of AOB. AOB has base 12 3 ft ft, or 24 3 ft and height 12 ft.

area of segment = 192 – To the nearest tenth, the area of the shaded segment is ft Use a calculator. Step 3: Subtract the area of AOB from the area of sector AOB to find the area of the segment of the circle. (continued)