Page 292 HW Answers

Learning Goal Assignments Our learning goal is to be able to solve for perimeter, area and volume. Learning Goal Assignments Perimeter and Area of Rectangles and Parallelograms Perimeter and Area of Triangles and Trapezoids The Pythagorean Theorem Circles Drawing Three-Dimensional figures Volume of Prisms and Cylinders Volume of Pyramids and Cones Surface Area of Prisms and Cylinders Surface Area of Pyramids and Cones Spheres

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

Pre-Algebra HOMEWORK Page 298 #1-18

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

Learning Goal Assignment 6-4 Circles Learning Goal Assignment 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 ft2

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