10-5 Circles Course 1 HOMEWORK & Learning Goal HOMEWORK & Learning Goal AIMS Prep AIMS Prep Lesson Presentation Lesson Presentation

Chapter 10 Section 4 6 th M. HOMEWORK Answers Page #1-4 and #11-14 (SR)

Chapter 10 Section 5 6 th Grade Math HOMEWORK Page 518 #6-9 (Circumference) & #10-12 (Area)

Our Learning Goal Students will be able to find the perimeter and area of polygons; find the area and circumference of circles and find the surface area and volume of 3D shapes.

Our Learning Goal Assignments Learn to find the perimeter and missing side lengths of a polygon. Learn to estimate the area of irregular figures and to find the area of rectangles, triangles, and parallelograms. Learn to break a polygon into simpler parts to find its area. Learn to make a model to explore how area and perimeter are affected by changes in the dimensions of a figure. Learn to identify the parts of a circle and to find the circumference and area of a circle. Learn to name solid figures. Learn to find the surface areas of prisms, pyramids, and cylinders. Learn to estimate and find the volumes of rectangular prisms and triangular prisms. Learn to find volumes of cylinders.

Warm Up The length and width of a rectangle are each multiplied by 5. Find how the perimeter and area of the rectangle change. The perimeter is multiplied by 5, and the area is multiplied by 25. Course Circles

Problem of the Day When using a calculator to find the height of a rectangle whose length one knew, a student accidentally multiplied by 20 when she should have divided by 20. The answer displayed was 520. What is the correct height? 1.3 Course Circles

Today’s Learning Goal Assignment Learn to identify the parts of a circle and to find the circumference and area of a circle. Course Circles

Vocabulary circle center radius (radii) diameter circumference pi Insert Lesson Title Here Course Circles

A circle is the set of all points in a plane that are the same distance from a given point, called the center. Center Course Circles

A line segment with one endpoint at the center of the circle and the other endpoint on the circle is a radius (plural: radii). Center Radius Course Circles

A chord is a line segment with both endpoints on a circle. A diameter is a chord that passes through the center of the circle. The length of the diameter is twice the length of the radius. Center Radius Diameter Course Circles

Additional Example 1: Naming Parts of a Circle Name the circle, a diameter, and three radii. N The circle is circle Z.LM is a diameter.ZL, ZM, and ZN are radii. M Z L Course Circles

Try This: Example 1 Name the circle, a diameter, and three radii. The circle is circle D.IG is a diameter.DI, DG, and DH are radii. G H D I Course Circles

The distance around a circle is called the circumference. Center Radius Diameter Circumference Course Circles

MATH/NUMBERSANDOPERATI ONS/PI/ BRAINPOP - Pi

The ratio of the circumference to the diameter,, is the same for any circle. This ratio is represented by the Greek letter , which is read “pi.” C d C d =  Course Circles

The formula for the circumference of a circle is C = d or C = 2r. The decimal representation of pi starts with and goes on forever without repeating. We estimate pi using either 3.14 or Course Circles

Additional Example 2A: Using the Formula for the Circumference of a Circle Find the missing value to the nearest hundredth. Use 3.14 for pi. A. d = 11 ft; C = ? C = dC  C  ft Write the formula. Replace  with 3.14 and d with ft Course Circles

Try This: Example 2A Find the missing value to the nearest hundredth. Use 3.14 for pi. A. d = 9 ft; C = ? C = dC  C  ft Write the formula. Replace  with 3.14 and d with 9. 9 ft Course Circles

Additional Example 2B: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. B. r = 5 cm; C = ? C = 2rC  C  31.4 cm Write the formula. Replace  with 3.14 and r with 5. 5 cm Course Circles

Try This: Example 2B Find each missing value to the nearest hundredth. Use 3.14 for pi. B. r = 6 cm; C = ? C = 2rC  C  cm Write the formula. Replace  with 3.14 and r with 6. 6 cm Course Circles

Additional Example 2C: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. C. C = cm; d = ? C = d  3.14d7.00 cm  d Write the formula. Replace C with and  with d _______  Divide both sides by Course Circles

Try This: Example 2C Find each missing value to the nearest hundredth. Use 3.14 for pi. C. C = cm; d = ? C = d  3.14d6.00 cm  d Write the formula. Replace C with and  with d _______  Divide both sides by Course Circles

The formula for the area of a circle is A = r 2 OR A = 3.14(r)(r) Course Circles

Additional Example 3: Using the Formula for the Area of a Circle Find the area of the circle. Use for pi. d = 42 cm; A = ? Write the formula to find the area. A = r 2 r = d ÷ 2r = 42 ÷ 2 = 21 The length of the diameter is twice the length of the radius. Replace  with and r with __ A  __ Use the GCF to simplify. 63 A  1,386 cm 2 Multiply A  cm Course Circles

Write the formula to find the area. A = r 2 r = d ÷ 2r = 28 ÷ 2 = 14 The length of the diameter is twice the length of the radius. Replace  with and r with __ A  __ Use the GCF to simplify. 28 A  616 cm 2 Multiply. Try This: Example 3 Find the area of the circle. Use for pi. d = 28 cm; A = ? 22 7 A  cm Course Circles

Don’t forget your proper heading! Trade & Grade! 10-5 Lesson Quiz Find the circumference and area of each circle. Use 3.14 for  Find the area of a circle with a diameter of 20 feet. Use 3.14 for . C = in. Insert Lesson Title Here C = in. 8 in. 314 ft 2 A = in 2 A = in 2 3 in. Course Circles

6 th Grade AIMS Prep Recall some test-taking tricks that you use to “win” on the AIMS Math. Use at least one to solve the following example!

AIMS Example 2