6-4 Circles Warm Up Problem of the Day Lesson Presentation Pre-Algebra

Pre-Algebra 6-4 Circles 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? 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? 13 ft

6-4 Circles Learn to find the area and circumference of circles.

Vocabulary circle radius diameter circumference

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.

d = 2r Radius Center The diameter d is twice the radius r. Diameter Circumference The circumference of a circle is the distance around the circle.

Remember! Pi (p) is an irrational number that is often approximated by the rational numbers 3.14 and . 22 7

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 = 2pr = 2p(4) = 8p m  25.1 m B. Circle with a diameter of 3.3 ft C = pd = p(3.3) = 3.3p ft  10.4 ft

Try This: Example 1 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 8 cm C = 2pr = 2p(8) = 16p cm  50.2 cm B. Circle with a diameter of 4.25 in. C = pd = p(4.25) = 4.25p in.  13.3 in.

Additional Example 2: Finding the Area of a Circle Find the area of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p. A. Circle with a radius of 4 in. A = pr2 = p(42) = 16p in2  50.2 in2 d 2 = 1.65 B. Circle with a diameter of 3.3 m A = pr2 = p(1.652) = 2.7225p m2  8.5 m2

Try This: Example 2 Find the area of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p. A. Circle with a radius of 8 cm A = pr2 = p(82) = 64p cm2  201.0 cm2 d 2 = 1.1 B. Circle with a diameter of 2.2 ft A = pr2 = p(1.12) = 1.21p ft2  3.8 m2

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 p and to the nearest tenth. Use 3.14 for p. A = pr2 C = pd = p(32) = p(6) = 9p units2 = 6p units  28.3 units2  18.8 units

Try This: Example 3 Graph the circle with center (–2, 1) that passes through (–2, 5). Find the area and circumference, both in terms of p and to the nearest tenth. Use 3.14 for p. y A = pr2 C = pd (–2, 5) = p(42) = p(8) 4 = 16p units2 = 8p units  50.2 units2  25.1 units x (–2, 1)

Additional Example 4: Measurement Application 22 7 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 p. C = pd = p(56) Find the circumference.  (56)  22 7 56 1 22 7  176 ft The distance is the circumference of the wheel times the number of revolutions, or about 176  15 = 2640 ft.

Find the circumference. 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 p. 22 7 C = pd = p(14) Find the circumference.  (14)  22 7 14 1 22 7 12 3 6 9  44 in. The distance is the circumference of the clock times the number of revolutions, or about 44  60 = 2640 in.

1. radius 5.6 m 11.2p m; 35.2 m 2. diameter 113 m 113p mm; 354.8 mm Lesson Quiz Find the circumference of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p. 1. radius 5.6 m 11.2p m; 35.2 m 2. diameter 113 m 113p mm; 354.8 mm Find the area of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p. 3. radius 3 in. 9p in2; 28.3 in2 4. diameter 1 ft 0.25p ft2; 0.8 ft2