IB DP Maths: AA SL復習筆記3.1.3 Arcs & Sectors
Length of an Arc
What is an arc?
- An arc is a part of the?circumference?of a circle
- It is easiest to think of it as the crust of a single slice of pizza
- The length of an arc depends of the size of the angle at the centre of the circle
- If the angle at the centre is?less than 180°?then the arc is known as a?minor arc
- This could be considered as the crust of a single slice of pizza
- If the angle at the centre is?more than 180°?then the arc is known as a?major arc
- This could be considered as the crust of the remaining pizza after a slice has been taken away
How do I find the length of an arc?
- The length of an arc is simply a fraction of the circumference of a circle
- The fraction can be found by dividing the angle at the centre by 360°
Exam Tip
- Make sure that you read the question carefully to determine if you need to calculate the arc length of a sector, the perimeter or something else that incorporates the arc length!
Worked Example
A circular pizza has had a slice cut from it, the angle of the slice that was cut was 38 °. The radius of the pizza is 12 cm. Find
i)? ? ? the length of the outside crust of the slice of pizza (the minor arc),
ii)? ? ?the perimeter of the remaining pizza.
Area of a Sector
What is a sector?
- A sector is a part of a circle enclosed by two radii (radiuses) and an arc
- It is easier to think of this as the shape of a single slice of pizza
- The area of a sector depends of the size of the angle at the centre of the sector
- If the angle at the centre is?less than 180°?then the sector is known as a?minor sector
- This could be considered as the shape of a single slice of pizza
- If the angle at the centre is?more than 180°?then the sector is known as a?major sector
- This could be considered as the shape of the remaining pizza after a slice has been taken away
How do I find the area of a sector?
Worked Example
Jamie has divided a circle of radius 50 cm into two sectors; a minor sector of angle 100° and a major sector of angle 260°. He is going to paint the minor sector blue and the major sector yellow. Find
i)? ? ? ?the area Jamie will paint blue,
ii)? ? ? the area Jamie will paint yellow.
Arcs & Sectors Using Radians
How do I use radians to find the length of an arc?
How do I use radians to find the area of a sector?
Worked Example
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