Lessons 6.5 Circumference and 8.5 Area of a Circle PI π = Ratio of Circumference to Diameter HOMEWORK: Lesson 6.5/1-13 Lesson 8.5/1-10

Pi (𝜋) is approximately ≈ 3.14 (or 22/7) Circumference C = 𝜋𝑑=2𝜋𝑟 Pi (𝜋) is approximately ≈ 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 = π x diameter For Example- Circumference= π * 10 C = 10π cm C ≈ 10*3.14 C ≈ 31,4 cm exact 10cm approx.

Example 1: The diameter of a circle is 3 centimeters. What is the circumference? Solution: C = π d C = 3 π cm exact C ≈ 3 (3.14) cm C ≈ 9.42 cm approx.

Example 2: The radius of a circle is 2 inches. What is the circumference? Solution: C = 2 π r C = 2 π 2 C = 4 π in exact C ≈ 4 * 3.14 C ≈ 12.56 in approx.

Example 3: The circumference of a circle is 15.7 centimeters. What is the diameter? Solution: 15.7 cm = πd 15.7 𝜋 cm = d exact d ≈ 15.7 3.14 d≈ 5 cm approx.

Example 4: The distance around a carousel is 21.98 yards. What is the radius? C = 2 π r 21.98 6.28 ≈ r 21.98 = 2 π r r≈ 3.5 yds 21.98 2𝜋 yds = r approx. exact

Finding the Area A=𝜋 𝑟 2 Area= π * radius2 Area= π * 72 = π * 49 A = 49 π 𝑐𝑚 2 (exact) A ≈ 49 * 3.14 A ≈ 153.86 𝑐𝑚 2 (approx) A ≈ 49 * π (π button) A ≈ 153.93804 𝐀 ≈ 153.94 𝑐𝑚 2 (approx) 7cm

Find the area of a circle given the diameter 𝐴=𝜋 𝑟 2 𝐴=𝜋 6 2 𝐴=36𝜋 𝑐𝑚 2 𝐴≈36∗3.14 𝐴≈113.04 𝑐𝑚 2

Circumference  Area If C = 25π cm Find Area 12.5𝑐𝑚=𝑟 𝐴=𝜋 𝑟 2 25𝜋=2𝜋𝑟 𝐴=𝜋 12.5 2 25𝜋=2𝜋𝑟 25=2𝑟 𝐴=156.25𝜋 𝑐𝑚 2 25 2 = 2 2 𝑟 exact 𝐴≈490.63 𝑐𝑚 2 approx. 12.5𝑐𝑚=𝑟

Circumference  Area If A = 144π 𝑐𝑚 2 Find circumference 12 𝑐𝑚=𝑟 144𝜋=𝜋 𝑟 2 𝐶=2𝜋𝑟 144𝜋=𝜋 𝑟 2 𝐶=2𝜋12 144= 𝑟 2 𝐶=24𝜋𝑐𝑚 exact 144 =𝑟 𝐶≈75.36 𝑐𝑚 12 𝑐𝑚=𝑟 approx.

Circumference  Area If A = 200.96 𝑐𝑚 2 Find circumference 8 𝑐𝑚=𝑟 200.96=𝜋 𝑟 2 𝐶=2𝜋8 200.96=3.14 𝑟 2 𝐶=16𝜋 cm exact 200.96 3.14 = 3.14 3.14 𝑟 2 𝐶≈16∗3.14𝑐𝑚 64= 𝑟 2 𝐶≈50.24 𝑐𝑚 64 =𝑟 approx. 8 𝑐𝑚=𝑟

Sketch and Solve What is the circumference of a 12-inch pizza? C= πd C= 12π in C≈ 12*3.14 in C≈ 37.68 in What is the surface area of the pizza? A = π 𝒓 𝟐  r=6 in A=36 π 𝑖𝑛 2 A ≈ 113.04 𝑖𝑛 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 = 2πr 𝟐𝟏.𝟗𝟖 𝟐(𝟑.𝟏𝟒) ≈𝒓 3.5yds ≈ 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 = πd 𝟕𝟖.𝟓 𝟑.𝟏𝟒 ≈𝒅 25 miles ≈ d

The area of a circle Use π = 3.14 to find the area of the following circles: 2 cm 10 m A = πr2 A = πr2 = 3.14 × 22 = 3.14 × 52 = 12.56 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 = πr2 A = πr2 = 3.14 × 232 = 3.14 × 392 = 1661.06 mm2 = 4775.94 cm2

A= π x r2 Finding the Area exact A=4π 𝑐𝑚 2 A≈ 12.56 𝑐𝑚 2 A=25π 𝑐𝑚 2 approx. A=100π 𝑐𝑚 2 A≈ 314 𝑐𝑚 2 A=49π 𝑐𝑚 2 A≈153.86 𝑐𝑚 2 A=32π 𝑐𝑚 2 , A≈ 100.48 𝑐𝑚 2 A= 36 πc 𝑚 2 A ≈ 113.04 𝑐𝑚 2