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.

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Presentation transcript:

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.

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

Learn to identify the parts of a circle and to find the circumference and area of a circle.

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

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

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

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

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

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

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

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 = 

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. 22 7

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

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

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 3.14.

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

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

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 3.14.

The formula for the area of a circle is A = r 2. A = r 2

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

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

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.