6-4 Circles Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation
Warm Up 1. Find the length of the hypotenuse of a right triangle that has legs 3 in. and 4 in. long. 2. The hypotenuse of a right triangle measures 17 in., and one leg measures 8 in. How long is the other leg? 3. To the nearest centimeter, what is the height of an equilateral triangle with sides 9 cm long? Course Circles 5 in. 15 in. 8 cm
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? Course Circles 13 ft
Learn to find the area and circumference of circles. Course Circles
Course Circles circle radius diameter circumference Vocabulary
Course 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 Circles Radius Center Diameter Circumference The diameter d is twice the radius r. d = 2r The circumference of a circle is the distance around the circle.
Course Circles
Course Circles Remember! Pi () is an irrational number that is often approximated by the rational numbers 3.14 and. 22 7
Course Circles Additional Example 1: Finding the Circumference of a Circle A. Circle with a radius of 4 m C = 2r = 2(4) = 8m 25.1 m B. Circle with a diameter of 3.3 ft C = d = (3.3) = 3.3ft 10.4 ft Find the circumference of each circle, both in terms of and to the nearest tenth. Use 3.14 for .
Course Circles Try This: Example 1 A. Circle with a radius of 8 cm C = 2r = 2(8) = 16cm 50.2 cm B. Circle with a diameter of 4.25 in. C = d = (4.25) = 4.25in. 13.3 in. Find the circumference of each circle, both in terms of and to the nearest tenth. Use 3.14 for .
Course Circles
Course Circles Additional Example 2: Finding the Area of a Circle A = r 2 = (4 2 ) = 16in 2 50.2 in 2 A. Circle with a radius of 4 in. Find the area of each circle, both in terms of and to the nearest tenth. Use 3.14 for . B. Circle with a diameter of 3.3 m A = r 2 = ( ) = m 2 8.5 m 2 d2d2 = 1.65
Course Circles B. Circle with a diameter of 2.2 ft A = r 2 = (1.1 2 ) = 1.21ft 2 3.8 m 2 d2d2 = 1.1 Try This: Example 2 Find the area of each circle, both in terms of and to the nearest tenth. Use 3.14 for . A = r 2 = (8 2 ) = 64cm 2 cm 2 A. Circle with a radius of 8 cm
Course Circles Additional Example 3: Finding the Area and Circumference on a Coordinate Plane A = r 2 = (3 2 ) = 9units 2 28.3 units 2 C = d = (6) = 6units 18.8 units 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
Course Circles Try This: Example 3 x y A = r 2 = (4 2 ) (–2, 1) = 16units 2 50.2 units 2 C = d = (8) = 8units 25.1 units 4 (–2, 5) Graph the circle with center (–2, 1) that passes through (–2, 5). Find the area and circumference, both in terms of and to the nearest tenth. Use 3.14 for
Course Circles Additional Example 4: Measurement Application C = d = (56) 176 ft (56) A Ferris wheel has a diameter of 56 feet and makes 15 revolutions per ride. How far would someone travel during a ride? Use for . Find the circumference The distance is the circumference of the wheel times the number of revolutions, or about 176 15 = 2640 ft.
Course Circles Try This: Example 4 A second hand on a clock is 7 in long. What is the distance it travels in one hour? Use for C = d = (14) (14) 22 7 Find the circumference. 44 in. The distance is the circumference of the clock times the number of revolutions, or about 44 60 = 2640 in
Course 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 2. diameter 113 m 11.2m; 35.2 m 113mm; mm Find the area of each circle, both in terms of and to the nearest tenth. Use 3.14 for . 3. radius 3 in. 4. diameter 1 ft 9in 2 ; 28.3 in ft 2 ; 0.8 ft 2