Mission 4: circles Missions 4.1 to 4.6

What is the significance of King Arthur’s round table?

Mission 4.1 – Intro to Circles

Mission 4.1 – intro to circles

Mission 4.1 – intro to circles Radius – The radius of a circle is the length of the line from the center to any point on its edge. Diameter – The diameter of a circle is the length of the line through the center and touching two points on its edge. Chord – A line that links two points on a circle or curve. Circumference – The distance around the edge of a circle. Arc – Two points lying on a circle actually define two arcs. The shortest is called the 'minor arc' the longer one is called the 'major arc'.

Mission 4.1 – intro to circles Area - …? Sector - The part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle. Central angle - A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Tangent - A line that contacts an arc or circle at only one point. Chord - A line that links two points on a circle or curve.

Mission 4.2 – construction of circles Find the center of a circle using two perpendicular lines and two chords. The point of intersection is the center of the circle.

Mission 4.2 – construction of circles Draw a circle using 3 circumference points: Find the centre of the circle first using perpendicular lines Place the compass on the center and create a circle that passes through all three points. Note: The distance from the center to each point should be the same

- Circles…it all comes together Radius Circumference Diameter mission 4.3 radius, diameter & circumference - Circles…it all comes together Radius Circumference Diameter R = d ÷ 2 R = C÷2÷π C = π x d C = 2 x π x r D = C÷π D = 2 x r

mission 4.3 radius, diameter & circumference Radius is half the diameter. Diameter is double the radius.

Mission 4.3 Circumference of a Circle Example: The diameter of a doughnut is 5.6cm. What is the circumference? C = π xd = 3.14 x 5.6 C = 17.6 cm

Mission 4.3 circumference of a circle Example 2 The radius of a large all dressed pizza at McEwen is 32cm. Find the length of the crust. C = 2 x π x r = 2 x 3.14 x 32 C = 200.96 cm

Mission 4.3 circumference of a circle Example 3 A circular crater has a circumference of 125.6km. If an astronaut is going to walk the greatest distance across the circle, how far will he be traveling? C = 125.6 d = C÷ π D = ? = 125.6 ÷ 3.14 d = 40 km The astronaut will walk 40 km across!

Mission 4.4 Arc length & circumference A circle with circumference of 68 m has an arc length of 10m. What central angle corresponds to this arc? central angle = arc length 360 circumference x = 10m 360 68m x = 53 degrees (Always round to the nearest whole degree)

Mission 4.4 Arc length & circumference Example 2 An arc with central angle of 78° has a length of 18.2cm. Find the radius of this circle. 78 ° = 18.2 cm 360 circumference Circumference = 84 cm r = C ÷ 3.14 ÷ 2 = 84 ÷ 3.14 ÷ 2 r = 13.4 cm

Mission 4.4 Arc length & circumference Example 3 A circle with a diameter of 89mm has an arc that corresponds to a central angle of 139°. Find the length of this arc. C = 3.14 x d 139° = arc = 3.14 x 89mm 360° 279.46 = 279.46mm arc = 107.9mm

Mission 4.5 AREA OF A CIRCLE Area = 3.14 x r2 OR πr² Example: Find the area of a circle with a radius of 7 m. A = 3.14 x 72 = 3.14 x 7 x 7 A = 153.86 m2

Mission 4.6 Calculating sector area To calculate the Sector Area we will use cross- multiplication: Sector Area = Central Angle Area 360º