Holt CA Course 1 9-4Circumference and Area Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

Holt CA Course 1 9-4Circumference and Area 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

Holt CA Course 1 9-4Circumference and Area MG2.1 Use formulas routinely for finding the perimeter and area of basic two- dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Also covered: MG3.2 California Standards

Holt CA Course 1 9-4Circumference and Area circumference Vocabulary

Holt CA Course 1 9-4Circumference and Area 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.

Holt CA Course 1 9-4Circumference and Area

Holt CA Course 1 9-4Circumference and Area Remember! Pi () is an irrational number that is often approximated by the rational numbers 3.14 and. 22 7

Holt CA Course 1 9-4Circumference and Area Additional Example 1: Finding the Circumference of a Circle A. circle with a radius of 4 m C = 2r = 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 Find the circumference of each circle, both in terms of  and to the nearest tenth. Use 3.14 for .

Holt CA Course 1 9-4Circumference and Area Check It Out! Example 1 A. circle with a radius of 8 cm C = 2r = 2(8) = 16cm  50.2 cm B. circle with a diameter of 4.25 in. C = d = (4.25) = 4.25in.  13.3 in. Find the circumference of each circle, both in terms of  and to the nearest tenth. Use 3.14 for .

Holt CA Course 1 9-4Circumference and Area

Holt CA Course 1 9-4Circumference and Area Additional Example 2: Finding the Area of a Circle A = r 2 = (4 2 ) = 16in 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

Holt CA Course 1 9-4Circumference and Area B. circle with a diameter of 2.2 ft A = r 2 = (1.1 2 ) = 1.21ft 2  3.8 ft 2 d2d2 = 1.1 Check It Out! 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 ) = 64cm 2  cm 2 A. circle with a radius of 8 cm

Holt CA Course 1 9-4Circumference and Area Additional Example 3: Finding the Area and Circumference on a Coordinate Plane A = r 2 = (3 2 ) = 9units 2  28.3 units 2 C = d = (6) = 6units  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 

Holt CA Course 1 9-4Circumference and Area Check It Out! Example 3 x y A = r 2 = (4 2 ) (–2, 1) = 16units 2  50.2 units 2 C = d = (8) = 8units  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 

Holt CA Course 1 9-4Circumference and Area 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.

Holt CA Course 1 9-4Circumference and Area Check It Out! 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

Holt CA Course 1 9-4Circumference and Area 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 11.2 m; 35.2 m 113 mm; 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 9 in 2 ; 28.3 in  ft 2 ; 0.8 ft 2