Download presentation

Presentation is loading. Please wait.

1
**Areas of Circles and Sectors**

Section 11.3 Areas of Circles and Sectors

2
In Lesson 10-1, you learned that the formula for the circumference C of a circle with radius r is given by C = 2πr. You can use this formula to develop the formula for the area of a circle. Below, a circle with radius r and circumference C has been divided into congruent pieces and then rearranged to form a figure that resembles a parallelogram. As the number of congruent pieces increases, the rearranged figure more closely approaches a parallelogram. The base of the parallelogram is 0.5C and the height is r, so its area is 0.5C • r. Since C = 2πr, the area of the parallelogram is also 0.5(2πr)r or πr2.

4
**The area of the cover is about 6082 square inches.**

Example 1: An outdoor accessories company manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches. The diameter of the umbrella is 72 inches, and the cover must extend 8 inches in each direction. So, the diameter of the cover is or 88 inches. Divide by 2 to find that the radius is 44 inches. A = πr2 Area of a circle = π(44)2 Substitution ≈ Use a calculator The area of the cover is about 6082 square inches.

5
**Example 2: Find the radius of a circle with an area of 58 square inches.**

A = πr2 Area of a circle 58 = πr2 Substitution Divide each side by π. Take the positive square root of each side. 4.3 ≈ r Simplify The radius of the circle is about 4.3 in.

6
**A slice of a circular pizza is an example of a sector of a circle**

A slice of a circular pizza is an example of a sector of a circle. A sector of a circle is a region of a circle bounded by a central angle and its intercepted major or minor arc. The formula for the area of a sector is similar to the formula for arc length.

7
Example 3: a) A pie has a diameter of 9 inches and is cut into 10 congruent slices. What is the area of one slice to the nearest hundredth? Find the arc measure of a pie slice. Since the pie is equally divided into 10 slices, each slice will have an arc measure of 360 ÷ 10 or 36. Find the radius of the pie. Use this measure to find the area of the sector, or slice. The diameter is 9 inches, so the radius is 4.5 inches. Area of a sector x = 36 and r = 4.5 ≈ 6.36 in.2 Use a calculator. The area of one slice of pie is about 6.36 square inches.

8
Example 3: b) A pizza has a diameter of 14 inches and is cut into 8 congruent slices. What is the area of one slice to the nearest hundredth? Find the arc measure of a pie slice. Since the pie is equally divided into 8 slices, each slice will have an arc measure of 360 ÷ 8 or 45. Find the radius of the pie. Use this measure to find the area of the sector, or slice. The diameter is 14 inches, so the radius is 7 inches. Area of a sector x = 45 and r = 7 ≈ in.2 Use a calculator. The area of one slice of pie is about square inches.

9
**Example 4: Find the area of the shaded sector**

Example 4: Find the area of the shaded sector. Round to the nearest tenth. a) Area of a sector x = 53 and r = 4 ≈ 7.4 ft2 Use a calculator.

10
**Example 4: Find the area of the shaded sector**

Example 4: Find the area of the shaded sector. Round to the nearest tenth. b) Area of a sector x = 295 and r = 11 ≈ in.2 Use a calculator.

Similar presentations

Presentation is loading. Please wait....

OK

Areas Advanced Geometry Areas and Volumes Lesson 1.

Areas Advanced Geometry Areas and Volumes Lesson 1.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on seven segment display pin Seven segment display ppt online Ppt on natural and artificial satellites of india Ppt on eisenmenger syndrome image Ppt online gambling addiction Ppt on file system in unix the lowest Ppt on minimum wages act mumbai Ppt on world book day character Cool backgrounds for ppt on social media Ppt on viruses and bacteria video