Do Now Take out your calculator. Take out your notebook. Find the length of arc AB.

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Presentation transcript:

Do Now Take out your calculator. Take out your notebook. Find the length of arc AB.

Announcements Circles test next Thursday/Friday Auction next Thursday/Friday Writing project starts next week

AREA OF ANNULUSES, SECTORS AND SEGMENTS

Today’s Objectives Discover formulas and methods for calculating the area of annuluses, sectors and segments of a circle. Write the equation of a circle. Transform a circle throughout the coordinate plane. Use problem solving skills

AnnulusSectorSegment The region between two concentric circles The region between two radii and an arc The region between a chord and an arc

Find the area of the annulus R=7 and r=4

Find the area of the sector

DO NOW: Find the area of the segment

Challenge Problem You share a 12” pizza with three friends. The crust is 1” wide. All three of your friends eat their crust. You don’t eat your crust. What is the area of the remaining crust?

CIRCLES IN THE COORDINATE PLANE

Write the equation for a circle… …centered at the origin with radius of 5. x 2 +y 2 =25. …centered at the origin with radius of 7. x 2 +y 2 =49. …centered at (3, 5) with radius of 7. (x-3) 2 +(y-5) 2 =49. …centered at (-5, 9) with radius of 4. (x+5) 2 +(y-9) 2 =16. What’s the pattern?

In general, the equation for a circle… …with center at (h,k) and radius r is (x-h) 2 + (y-k) 2 = r 2

Practice What is the radius of ◦ x 2 +y 2 =81 ◦ (x+4) 2 +(y-2) 2 =36 What is the center of ◦ x 2 +y 2 =81 ◦ (x+4) 2 +(y-2) 2 =36

Practice Write the equation for a circle whose radius is 7 and whose center is (0, 0)? radius is 5 and whose center is (1, 4)? radius is 3 and whose center is (-2, 6)? radius is 10 and whose center is (-5, -7)? radius is 8 and whose center is (1, -8)? radius is 1 and whose center is (0, 0)?

Today’s Objectives Discover formulas and methods for calculating the area of annuluses, sectors and segments of a circle. Write the equation of a circle. Transform a circle throughout the coordinate plane. Use problem solving skills

Exit slip 1. Identify the radius and the center of the circle (x-5) 2 +(y+3) 2 = Write the equation for a circle whose radius is 7 and center is (6,-3) 3. Find the area of the sector below.