# Lessons 6.5 Circumference and 8.5 Area of a Circle

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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

Pi (π) is approximately β 3.14 (or 22/7)
Circumference C = ππ=2ππ Pi (π) is approximately β 3.14 (or 22/7) Pi is exactly = π

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.

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.

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.

Example 3: The circumference of a circle is 15.7 centimeters.
What is the diameter? Solution: 15.7 cm = Οd 15.7 π cm = d exact d β dβ 5 cm approx.

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

Finding the Area A=π π 2 Area= Ο * radius2 Area= Ο * 72 = Ο * 49
A = 49 Ο ππ 2 (exact) A β 49 * 3.14 A β ππ 2 (approx) A β 49 * Ο (Ο button) A β π β ππ 2 (approx) 7cm

Find the area of a circle
given the diameter π΄=π π 2 π΄=π 6 2 π΄=36π ππ 2 π΄β36β3.14 π΄β ππ 2

Circumference οο  Area If C = 25Ο cm Find Area 12.5ππ=π π΄=π π 2 25π=2ππ
π΄=π 25π=2ππ 25=2π π΄=156.25π ππ 2 25 2 = 2 2 π exact π΄β ππ 2 approx. 12.5ππ=π

Circumference οο  Area If A = 144Ο ππ 2 Find circumference 12 ππ=π
144π=π π 2 πΆ=2ππ 144π=π π 2 πΆ=2π12 144= π 2 πΆ=24πππ exact 144 =π πΆβ ππ 12 ππ=π approx.

Circumference οο  Area If A = 200.96 ππ 2 Find circumference 8 ππ=π
200.96=π π 2 πΆ=2π8 200.96=3.14 π 2 πΆ=16π cm exact = π 2 πΆβ16β3.14ππ 64= π 2 πΆβ ππ 64 =π approx. 8 ππ=π

Sketch and Solve What is the circumference of a 12-inch pizza? C= Οd
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 ππ 2 A β ππ 2 exact 12 in approx. exact approx.

The distance around a carousel is 21.98 yards. What is the radius?
C=21.98yds 21.98 = 2Οr ππ.ππ π(π.ππ) βπ 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 = Οd ππ.π π.ππ βπ 25 miles β d

The area of a circle Use Ο = 3.14 to find the area of the following circles: 2 cm 10 m A = Οr2 A = Οr2 = 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 = Οr2 A = Οr2 = 3.14 Γ 232 = 3.14 Γ 392 = mm2 = cm2

A= Ο x r2 Finding the Area exact A=4Ο ππ 2 Aβ 12.56 ππ 2 A=25Ο ππ 2
approx. A=100Ο ππ 2 Aβ 314 ππ 2 A=49Ο ππ 2 Aβ ππ 2 A=32Ο ππ 2 , Aβ ππ 2 A= 36 Οc π 2 A β ππ 2