Calculating sector areas and arc lengths. Look at these relationships. What do you notice? Radius = R π R/2 R π 3 π R/2 2 π R 90 180270 360 Degrees Circumference.

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Presentation transcript:

Calculating sector areas and arc lengths

Look at these relationships. What do you notice? Radius = R π R/2 R π 3 π R/2 2 π R Degrees Circumference / arc

What do you notice? 2πR/360 What is π/36 = 10π/360 How can we use = π/36 this fact? 2πR/360 What is π/45 = 8π/360 how can we use = π/45 this fact? 3πR/2 ÷ 270 = 7.5π/270 = π/36 3πR/2 ÷ 270 = 6π/270 = π/45 Rπ / 180 = 5π/180 = π/36 Rπ / 180 = 4π/180 = π/45 Rπ/2 ÷ 90 = 5π/2 ÷ 90 = 2.5π÷90 = π/36 Rπ/2 ÷ 90 = 4π/2 ÷ 90 = 2π÷90 = π/45 Let R = you decide Let R = 5cmLet R = 4 cm

Lets look at some questions? Strategy Answer Put answer into context of question. Calculation 1.Turn into equivalent fractions with ? on the top. 2.Multiply by both sides by what ever is dividing the ? Lines to extract information. Put in the information you know. Question How long is the arc, when the angle at the centre is 125 o and the radius is 4.8cm? 2πR2πR ? Deg. Arc

Question How long is the arc, when the angle at the centre is 125 o and the radius is 4.8cm? Lines to extract information. Put in the information you know. 2 π ? Deg. Arc

Turn into equivalent fractions, with the ? on top and then multiply both sides by whatever is dividing the ? Lines to extract information. Put in the information you know. 2 π ? Deg. Arc

Lets look at some questions? Strategy Answer Put answer into context of question. The arc is 10.47cm when the radius is 4.8cm and the angle at the centre is 125 o Calculation Lines to extract information. Put in the information you know. Question How long is the arc, when the angle at the centre is 125 o and the radius is 4.8cm? 2 π ? Deg. Arc

Look at these area and degree relationships. What do you notice? Radius = R ¼ πR 2 ½ π R 2 3 / 4 π R 2 πR Degrees Area of a circle

What do you notice? πR 2 /360 What is π/10 = 36π/360 How can we use = π/10 this fact? πR 2 /360 What is 2π/45 = 16π/360 how can we use = 2π/45 this fact? 3 / 4 π R 2 ÷ 270 = 27π/270 = π/10 3 / 4 π R 2 ÷ 270 = 12π/270 =2π/45 R 2 π/2 ÷ 180 = 18π/180 = π/10 R 2 π/2 / 180 = 8π/180 = 2π/45 R 2 π/4÷ 90 = 36π/4 ÷ 90 = 9π/90 =π/10 R 2 π/4 ÷ 90 = 4π/90 = 2π/45 Let R = you decide Let R = 6cmLet R = 4 cm

Lets look at some questions? Strategy Answer Put answer into context of question. Calculation 1.Turn into equivalent fractions with ? on the top. 2.Multiply by both sides by what ever is dividing the ? Lines to extract information. Put in the information you know. Question What is the area of the sector, when the angle at the centre is 125 o and the radius is 4.8cm? πR2πR ? Deg. Arc

Question What is the area of the sector, when the angle at the centre is 125 o and the radius is 4.8cm? Lines to extract information. Put in the information you know. π ? Deg. area

Turn into equivalent fractions, with the ? on top and then multiply both sides by whatever is dividing the ? Lines to extract information. Put in the information you know. π ? Deg. Arc

When you do some questions. The strategy is: Question What is the area of the sector, when the angle at the centre is 125 o and the radius is 4.8cm? Calculation start with equivalent fractions! πR2πR ? Deg. Arc Answer Put answer into context of question. The area of the sector is approx cm 2 when the radius is 4.8cm and the degree at the centre is 125 o Lines to extract information. Put in the information you know.