Arcs and sectors
A sector is a slice of a circle, like a pizza wedge. An arc is the curved edge of that slice. Both are fractions of the whole circle.
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Analogy
Like cutting a pie: a quarter of the pie has a quarter of the area and a quarter of the crust.
Example
Fraction = 90 / 360 = 1/4Area = 1/4 x pi x 6^2 = 9 x pi = 28.3Arc = 1/4 x 2 x pi x 6 = 3 x pi = 9.4
In practice
Pie charts are built from sectors, and each angle shows a share of the total.
Practice
Flashcards
- What fraction of a circle is a 90 degree sector?One quarter, because 90 / 360 = 1/4.
Questions people ask
How do you find the area of a sector?
Work out the fraction of the circle: the angle divided by 360. Then multiply that fraction by the area of the whole circle, pi x r^2. A 90 degree sector is 1/4 of the circle, so it takes a quarter of the area.
What is the difference between an arc and a sector?
An arc is only the curved line along the edge, so its length is part of the circumference. A sector is the whole slice, including the area inside between the two straight radii. You find arc length and sector area using the same fraction.