Find the area of a circle with the given measure.

Slides:



Advertisements
Similar presentations
Areas of Circles and Sectors
Advertisements

Warm-Up Exercises Simplify the expression. ANSWER 1 8 3π3π (9π)
Using Radius to Find Circumference
AREA AND CIRCUMFERENCE OF A CIRCLE. diameter radius circumference The perimeter of a circle is called the circumference (C). The diameter (d) of a circle.
How do I find the surface area and volume of a sphere?
MM2G4 Students will use apply surface area and volume of a sphere. MM2G4 a Use and apply the area and volume of a sphere. MM2G4 b Determine the effect.
EXAMPLE 1 Use the formula for circumference Find the indicated measures. Write circumference formula. Substitute 9 for r. Simplify. Use a calculator. =
EXAMPLE 1 Use the formula for area of a circle Find the indicated measure. a. Area r = 2.5 cm SOLUTION Write formula for the area of a circle. = π (2.5)
EXAMPLE 1 Use the formula for circumference Find the indicated measures. Write circumference formula. Substitute 9 for r. Simplify. Use a calculator. =
Find the area of each circle.
MM2G3 Students will understand properties of circles. MM2G3 c Use the properties of circles to solve problems involving the length of an arc and the area.
EXAMPLE 1 Use the formula for area of a circle Find the indicated measure. a. Area r = 2.5 cm SOLUTION Write formula for the area of a circle. = π (2.5)
Answers to homework problems – page 8
EXAMPLE 1 Rewrite a formula with two variables Solve the formula C = 2πr for r. Then find the radius of a circle with a circumference of 44 inches. SOLUTION.
Areas of Circles and Sectors
AREAS OF CIRCLES AND SECTORS
EXAMPLE 3 Use the Area of a Sector Theorem Use the diagram to find the area of V. SOLUTION Area of sector TVU = Area of V m TU 360 ° Write formula for.
Areas of Circles and Sectors 11.5 California State Standards 8: Solve problems involving perimeter and area. 19: Use trigonometric functions 21: Prove.
11.4 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Circumference and Arc Length.
Use the formula for circumference
Chapter 11.5 Notes: Areas of Circles and Sectors Goal: You will find the areas of circles and sectors.
11.5 Areas of Circles and Sectors Geometry Ms. Reser.
Find the surface area of a sphere
Warm-Up 1.Find the circumference of a circle with a diameter of 10ft. Round your answer to the nearest tenth. 2.Find the circumference of  A if the radius.
Areas of Circles and Sectors
EXAMPLE 1 Rewrite a formula with two variables Solve the formula C = 2πr for r. Then find the radius of a circle with a circumference of 44 inches. SOLUTION.
Surface Area of Pyramids and Cones
Find the area of a circle with the given measure.
EXAMPLE 1 Use the formula for circumference Find the indicated measures. Write circumference formula. Substitute 9 for r. Simplify. Use a calculator.
Circumference and Area of Circles Section 8.7. Goal Find the circumference and area of circles.
Find the area of each circle.
Find the area of each polygon or circle.
Find the area of each polygon or circle.
10.5 Areas of Circles and Sectors
Do Now Agenda Homework Handout (10 problems)  Do Do Now!
Solve Problems Involving the Circumference and Area of Circles
11.5 Areas of Circles and Sectors
Area of Composite Shapes
Area of Composite Shapes
Find the area of each polygon or circle.
Volume of Prisms and Cylinders
Circumference, Area, and Volume
Measurement Warm-up Stringing Lights Powerpoint Squaring a Circle
7-7 Areas of Circles and Sectors
EXAMPLE 1 Find the perimeter and area of a rectangle Basketball
11.4 Circumference and Arc Length
0-8: Area.
11.6 Arc Lengths and Areas of Sectors
11.3 Areas of Circles and Sectors
11.1 Circumference and Arc Length 11.2 Areas of Circles and Sectors
Areas of Circles and Sectors
Warm UP! Circle O has a radius of 20 feet. What is the length of arc KL? K 65o O L 20 ft.
11.2 Areas of Sectors and circles
Find the surface area of a sphere
11.5 Areas of Circles and Sectors
AREAS OF CIRCLES AND SECTORS
Section 11.4 Circumference and Arc Length Theorem
DRILL HANDOUT.
11.4 Circumference and Arc Length
Find the surface area of a sphere
Warm UP! Circle O has a radius of 20 feet. What is the length of arc KL? K 65o O L 20 ft.
Objectives Learn and apply the formula for the volume of a sphere.
Semicircle basics.
Finding Arc Lengths and Areas of Sectors
6.8 Areas of Circles & Sectors
11.5 Areas of Circles and Sectors
6.8 Areas of Circles & Sectors
Essential Questions: Standards:
Warm up: Solve for x 1.) 2.) 4.) 3.) 124◦ 70◦ x 18◦ x 260◦ x 20◦ 110◦
Unit 4B Measure Figures Lesson 2 Area of Circles.
Presentation transcript:

Find the area of a circle with the given measure. 2. Radius: 1 3 mi 1. Radius: 8 cm ANSWER about 201.06 cm2 ANSWER about 5.59 mi2 4. Solve x2 = 100 π . 3. Circumference: 4π ft ANSWER 4π ft2 ANSWER about _ + 5.64

Vocabulary   Sector of a circle – the region bounded by two radii of the circle and their intercepted arc Area of a Sector Theorem 11.2 – area of sector : area of circle = arc measure : 360

Use the formula for area of a circle EXAMPLE 1 Use the formula for area of a circle Find the indicated measure. SOLUTION a. Area r = 2.5 cm A = πr2 Write formula for the area of a circle. = π (2.5)2 Substitute 2.5 for r. = 6.25π Simplify. ≈ 19.63 Use a calculator. The area of A is about 19.63 square centimeters. ANSWER

Use the formula for area of a circle EXAMPLE 1 Use the formula for area of a circle Find the indicated measure. SOLUTION A = 113.1 cm2 b. Diameter A = πr2 Write formula for the area of a circle. 113.1 = πr2 Substitute 113.1 for A. = r2 113.1 π Divide each side by π. 6 ≈ r Find the positive square root of each side. The radius is about 6 cm, so the diameter is about 12 centimeters. ANSWER

Find the areas of the sectors formed by UTV. EXAMPLE 2 Find areas of sectors Find the areas of the sectors formed by UTV. SOLUTION STEP 1 Find the measures of the minor and major arcs. Because m UTV = 70° , mUV = 70° and mUSV = 360° – 70° = 290°. STEP 2 Find the areas of the small and large sectors. Area of small sector = πr2 mUV 360° Write formula for area of a sector. = π 82 70° 360° Substitute. ≈ 39.10 Use a calculator.

Area of large sector = πr2 mUSV 360° EXAMPLE 2 Find areas of sectors Area of large sector = πr2 mUSV 360° Write formula for area of a sector. = π 82 290° 360° Substitute. ≈ 161.97 Use a calculator. The areas of the small and large sectors are about 39.10 square units and 161.97 square units, respectively. ANSWER

GUIDED PRACTICE for Examples 1 and 2 Use the diagram to find the indicated measure. about 615.75 ft2 ANSWERS 1. Area of D Area of red sector about 205.25 ft2 Area of blue sector about 410.50 ft2

Use the Area of a Sector Theorem EXAMPLE 3 Use the Area of a Sector Theorem Use the diagram to find the area of V. SOLUTION Area of sector TVU = Area of V mTU 360° Write formula for area of a sector. 35 = Area of V 40° 360° Substitute. 315 = Area of V Solve for Area of V. The area of V is 315 square meters. ANSWER

EXAMPLE 4 Standardized Test Practice SOLUTION The area you need to paint is the area of the rectangle minus the area of the entrance. The entrance can be divided into a semicircle and a square.

EXAMPLE 4 Standardized Test Practice 180° = 36(26) – (π 82 ) + 162 360° = 936 – [32π + 256] ≈ 579.47 The area is about 579 square feet. The correct answer is C. ANSWER

GUIDED PRACTICE for Examples 3 and 4 4. Find the area of H. 5. Find the area of the figure. about 907.92 cm2 ANSWER about 43.74 m2 ANSWER

GUIDED PRACTICE for Examples 3 and 4 6. If you know the area and radius of a sector of a circle, can you find the measure of the intercepted arc? Explain. Yes; the formula for the area of sector is m A = and if you solve this for m, you get m = 360 π r2 360A . ANSWER

Daily Homework Quiz Find the area of the sectors formed by DEF. Use the area of the sector to find the area of R ANSWER 106.03 in.2, 141.31 in.2 ANSWER 211.09 cm2

Daily Homework Quiz 3. Find the area of the shaded region. ANSWER 23.18 ft2