Areas of Circles and Sectors LESSON 11–3 Areas of Circles and Sectors

Five-Minute Check (over Lesson 11–2) TEKS Then/Now New Vocabulary Key Concept: Area of a Circle Example 1: Real-World Example: Area of a Circle Example 2: Use the Area of a Circle to Find a Missing Measure Key Concept: Area of a Sector Example 3: Real-World Example: Area of a Sector Lesson Menu

Find the area of the figure. Round to the nearest tenth if necessary. A. 202 units2 B. 198 units2 C. 62.7 units2 D. 28.4 units2 5-Minute Check 1

Find the area of the figure. Round to the nearest tenth if necessary. A. 96 units2 B. 92.4 units2 C. 83.1 units2 D. 81.8 units2 5-Minute Check 2

Find the area of the figure. Round to the nearest tenth if necessary. A. 70 units2 B. 72.5 units2 C. 75 units2 D. 77.5 units2 5-Minute Check 3

Find the area of the figure. Round to the nearest tenth if necessary. A. 58.5 units2 B. 117 units2 C. 198 units2 D. 234 units2 5-Minute Check 4

Trapezoid LMNO has an area of 55 square units. Find the height. A. 6 units B. 5 units C. 4 units D. 3 units 5-Minute Check 5

The area of a kite is 120 square meters The area of a kite is 120 square meters. The length of one diagonal is 15 meters. Find the length of the other diagonal. A. 4 m B. 8 m C. 16 m D. 1800 m 5-Minute Check 6

Mathematical Processes G.1(A), G.1(E) Targeted TEKS G.11(B) Determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure. G.12(C) Apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems. Mathematical Processes G.1(A), G.1(E) TEKS

You found the circumference of a circle. Find areas of circles. Find areas of sectors of circles. Then/Now

sector of a circle segment of a circle Vocabulary

Concept 1

Area of a Circle MANUFACTURING 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 8 + 72 + 8 or 88 inches. Divide by 2 to find that the radius is 44 inches. Example 1

Answer: The area of the cover is about 6082 square inches. Area of a Circle Area of a circle Substitution Use a calculator. Answer: The area of the cover is about 6082 square inches. Example 1

A swimming pool company manufactures circular covers for above ground pools. If the cover is 1 foot longer than the pool on each side, find the area of the cover. A. 62.8 ft2 B. 254.5 ft2 C. 314.2 ft2 D. 1256.6 ft2 Example 1

ALGEBRA Find the radius of a circle with an area of 58 square inches. Use the Area of a Circle to Find a Missing Measure ALGEBRA Find the radius of a circle with an area of 58 square inches. Area of a circle Substitution Divide each side by . Take the positive square root of each side. = r Simplify. 4.3 ≈ r Answer: The radius of the circle is about 4.3 in. Example 2

ALGEBRA Find the radius of a circle with an area of 45 square inches. A. 3.8 in. B. 4.5 in. C. 5.7 in. D. 7.6 in. Example 2

Concept 2

Step 1 Find the arc measure of a pie slice. Area of a Sector PIE 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? Step 1 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. Step 2 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. Example 3

Answer: The area of one slice of pie is about 6.36 square inches. Area of a Sector Area of a sector x = 36 and r = 4.5 Use a calculator. Answer: The area of one slice of pie is about 6.36 square inches. Example 3

PIZZA 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? A. 16.21 in2 B. 19.24 in2 C. 26.43 in2 D. 38.48 in2 Example 3

Areas of Circles and Sectors LESSON 11–3 Areas of Circles and Sectors