Presentation on theme: "Lessons 6.5 Circumference and 8.5 Area of a Circle"— Presentation transcript:
1 Lessons 6.5 Circumference and 8.5 Area of a Circle PI π = Ratio of Circumference to DiameterHOMEWORK: Lesson 6.5/1-13Lesson 8.5/1-10
2 Pi (𝜋) is approximately ≈ 3.14 (or 22/7) CircumferenceC = 𝜋𝑑=2𝜋𝑟Pi (𝜋) is approximately ≈ 3.14 (or 22/7)Pi is exactly = 𝝅
3 Finding the Circumference You can find the circumference of a circle by using the formula-Circumference = π x diameterFor Example-Circumference= π * 10C = 10π cmC ≈ 10*3.14C ≈ 31,4 cmexact10cmapprox.
4 Example 1: The diameter of a circle is 3 centimeters. What is the circumference?Solution:C = π dC = 3 π cmexactC ≈ 3 (3.14) cmC ≈ 9.42 cmapprox.
5 Example 2: The radius of a circle is 2 inches. What is the circumference?Solution:C = 2 π rC = 2 π 2C = 4 π inexactC ≈ 4 * 3.14C ≈ inapprox.
6 Example 3: The circumference of a circle is 15.7 centimeters. What is the diameter?Solution:15.7 cm = πd15.7 𝜋 cm = dexactd ≈d≈ 5 cmapprox.
7 Example 4:The distance around a carousel is yards. What is the radius?C = 2 π r≈ r21.98 = 2 π rr≈ 3.5 yds𝜋 yds = rapprox.exact
9 Find the area of a circle given the diameter𝐴=𝜋 𝑟 2𝐴=𝜋 6 2𝐴=36𝜋 𝑐𝑚 2𝐴≈36∗3.14𝐴≈ 𝑐𝑚 2
10 Circumference Area If C = 25π cm Find Area 12.5𝑐𝑚=𝑟 𝐴=𝜋 𝑟 2 25𝜋=2𝜋𝑟 𝐴=𝜋25𝜋=2𝜋𝑟25=2𝑟𝐴=156.25𝜋 𝑐𝑚 225 2 = 2 2 𝑟exact𝐴≈ 𝑐𝑚 2approx.12.5𝑐𝑚=𝑟
11 Circumference Area If A = 144π 𝑐𝑚 2 Find circumference 12 𝑐𝑚=𝑟 144𝜋=𝜋 𝑟 2𝐶=2𝜋𝑟144𝜋=𝜋 𝑟 2𝐶=2𝜋12144= 𝑟 2𝐶=24𝜋𝑐𝑚exact144 =𝑟𝐶≈ 𝑐𝑚12 𝑐𝑚=𝑟approx.
12 Circumference Area If A = 200.96 𝑐𝑚 2 Find circumference 8 𝑐𝑚=𝑟 200.96=𝜋 𝑟 2𝐶=2𝜋8200.96=3.14 𝑟 2𝐶=16𝜋 cmexact= 𝑟 2𝐶≈16∗3.14𝑐𝑚64= 𝑟 2𝐶≈ 𝑐𝑚64 =𝑟approx.8 𝑐𝑚=𝑟
13 Sketch and Solve What is the circumference of a 12-inch pizza? C= πd C= 12π inC≈ 12*3.14 inC≈ inWhat is the surface area of the pizza?A = π 𝒓 𝟐 r=6 inA=36 π 𝑖𝑛 2A ≈ 𝑖𝑛 2exact12 inapprox.exactapprox.
14 The distance around a carousel is 21.98 yards. What is the radius? C=21.98yds21.98 = 2πr𝟐𝟏.𝟗𝟖 𝟐(𝟑.𝟏𝟒) ≈𝒓3.5yds ≈ rAn asteroid hit the earth and created a huge round crater. Scientists measured the distance around the crater as 78.5 miles. What is the diameter of the crater?C=78.5yds78.5 = πd𝟕𝟖.𝟓 𝟑.𝟏𝟒 ≈𝒅25 miles ≈ d
15 The area of a circleUse π = 3.14 to find the area of the following circles:2 cm10 mA = πr2A = πr2= 3.14 × 22= 3.14 × 52= cm2= 78.5 m223 mmExplain that rather than use the formula on the previous slide, it is usually easier to halve the diameter mentally to give the radius, before substituting it into the formula.The most common error is to neglect to half the diameter to find the radius and to substitute this value into the formula. Ensure that pupils do not make this mistake.78 cmA = πr2A = πr2= 3.14 × 232= 3.14 × 392= mm2= cm2