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**Lessons 6.5 Circumference and 8.5 Area of a Circle**

PI Ο = Ratio of Circumference to Diameter HOMEWORK: Lesson 6.5/1-13 Lesson 8.5/1-10

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**Pi (π) is approximately β 3.14 (or 22/7)**

Circumference C = ππ=2ππ Pi (π) is approximately β 3.14 (or 22/7) Pi is exactly = π

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**Finding the Circumference**

You can find the circumference of a circle by using the formula- Circumference = Ο x diameter For Example- Circumference= Ο * 10 C = 10Ο cm C β 10*3.14 C β 31,4 cm exact 10cm approx.

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**Example 1: The diameter of a circle is 3 centimeters.**

What is the circumference? Solution: C = Ο d C = 3 Ο cm exact C β 3 (3.14) cm C β 9.42 cm approx.

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**Example 2: The radius of a circle is 2 inches.**

What is the circumference? Solution: C = 2 Ο r C = 2 Ο 2 C = 4 Ο in exact C β 4 * 3.14 C β in approx.

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**Example 3: The circumference of a circle is 15.7 centimeters.**

What is the diameter? Solution: 15.7 cm = Οd 15.7 π cm = d exact d β dβ 5 cm approx.

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Example 4: The distance around a carousel is yards. What is the radius? C = 2 Ο r β r 21.98 = 2 Ο r rβ 3.5 yds π yds = r approx. exact

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**Finding the Area A=π π 2 Area= Ο * radius2 Area= Ο * 72 = Ο * 49**

A = 49 Ο ππ 2 (exact) A β 49 * 3.14 A β ππ 2 (approx) A β 49 * Ο (Ο button) A β π β ππ 2 (approx) 7cm

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**Find the area of a circle**

given the diameter π΄=π π 2 π΄=π 6 2 π΄=36π ππ 2 π΄β36β3.14 π΄β ππ 2

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**Circumference οο Area If C = 25Ο cm Find Area 12.5ππ=π π΄=π π 2 25π=2ππ**

π΄=π 25π=2ππ 25=2π π΄=156.25π ππ 2 25 2 = 2 2 π exact π΄β ππ 2 approx. 12.5ππ=π

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**Circumference οο Area If A = 144Ο ππ 2 Find circumference 12 ππ=π**

144π=π π 2 πΆ=2ππ 144π=π π 2 πΆ=2π12 144= π 2 πΆ=24πππ exact 144 =π πΆβ ππ 12 ππ=π approx.

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**Circumference οο Area If A = 200.96 ππ 2 Find circumference 8 ππ=π**

200.96=π π 2 πΆ=2π8 200.96=3.14 π 2 πΆ=16π cm exact = π 2 πΆβ16β3.14ππ 64= π 2 πΆβ ππ 64 =π approx. 8 ππ=π

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**Sketch and Solve What is the circumference of a 12-inch pizza? C= Οd**

C= 12Ο in Cβ 12*3.14 in Cβ in What is the surface area of the pizza? A = Ο π π ο r=6 in A=36 Ο ππ 2 A β ππ 2 exact 12 in approx. exact approx.

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**The distance around a carousel is 21.98 yards. What is the radius?**

C=21.98yds 21.98 = 2Οr ππ.ππ π(π.ππ) βπ 3.5yds β r An 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=78.5yds 78.5 = Οd ππ.π π.ππ βπ
25 miles β d

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The area of a circle Use Ο = 3.14 to find the area of the following circles: 2 cm 10 m A = Οr2 A = Οr2 = 3.14 Γ 22 = 3.14 Γ 52 = cm2 = 78.5 m2 23 mm Explain 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 cm A = Οr2 A = Οr2 = 3.14 Γ 232 = 3.14 Γ 392 = mm2 = cm2

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**A= Ο x r2 Finding the Area exact A=4Ο ππ 2 Aβ 12.56 ππ 2 A=25Ο ππ 2**

approx. A=100Ο ππ 2 Aβ 314 ππ 2 A=49Ο ππ 2 Aβ ππ 2 A=32Ο ππ 2 , Aβ ππ 2 A= 36 Οc π 2 A β ππ 2

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