Transcript 3CH8L3
8-3 Circles Warm Up 1. Find the length of the hypotenuse of a right triangle that has legs 3 in. and 4 in. long. 5 in. 2. The hypotenuse of a right triangle measures 17 in., and one leg measures 8 in. How long is the other leg? 15 in. 3. To the nearest centimeter, what is the height of an equilateral triangle with sides 9 cm long? 8 cm Course 3 8-3 Circles Problem of the Day A rectangular box is 3 ft. by 4 ft. by 12 ft. What is the distance from a top corner to the opposite bottom corner? 13 ft Course 3 8-3 Circles TB P. 400-403 Learn to find the circumference and area of circles. Course 3 8-3 Circles Vocabulary circle radius diameter circumference Course 3 8-3 Circles A circle is the set of points in a plane that are a fixed distance from a given point, called the center. A radius connects the center to any point on the circle, and a diameter connects two points on the circle and passes through the center. Course 3 8-3 Circles Radius Center Diameter The diameter d is twice the radius r. d = 2r Circumference The circumference of a circle is the distance around the circle. Course 3 8-3 Circles Course 3 8-3 Circles Remember! Pi () is an irrational number that is often approximated by the rational numbers 3.14 and 22 . 7 Course 3 8-3 Circles Additional Example 1: Finding the Circumference of a Circle Find the circumference of each circle, both in terms of and to the nearest tenth. Use 3.14 for . A. Circle with a radius of 4 m C = 2r = 2(4) = 8 m 25.1 m B. Circle with a diameter of 3.3 ft C = d = (3.3) = 3.3 ft 10.4 ft Course 3 8-3 Circles Course 3 8-3 Circles Additional Example 2: Finding the Area of a Circle Find the area of each circle, both in terms of and to the nearest tenth. Use 3.14 for . A. Circle with a radius of 4 in. A = r2 = (42) = 16 in2 50.2 in2 B. Circle with a diameter of 3.3 m A = r2 = (1.652) = 2.7225 m2 8.5 m2 Course 3 d = 1.65 2 8-3 Circles Additional Example 3: Finding the Area and Circumference on a Coordinate Plane Graph the circle with center (–2, 1) that passes through (1, 1). Find the area and circumference, both in terms of and to the nearest tenth. Use 3.14 for . A = r2 Course 3 C = d = (32) = (6) = 9 units2 = 6 units 28.3 units2 18.8 units 8-3 Circles Additional Example 4: Measurement Application A Ferris wheel has a diameter of 56 feet and makes 15 revolutions per ride. How far would someone travel during a ride? Use 22 7 for . C = d = (56) 22 (56) 7 Find the circumference. 22 56 176 ft 7 1 The distance is the circumference of the wheel times the number of revolutions, or about 176 15 = 2640 ft. Course 3 8-3 Circles Lesson Quiz Find the circumference of each circle, both in terms of and to the nearest tenth. Use 3.14 for . 1. radius 5.6 m 11.2 m; 35.2 m 2. diameter 113 m 113 mm; 354.8 mm Find the area of each circle, both in terms of and to the nearest tenth. Use 3.14 for . 3. radius 3 in. 9 in2; 28.3 in2 4. diameter 1 ft 0.25 ft2; 0.8 ft2 Course 3