Geometry - Circles, Arcs, and Sectors
6 important questions on Geometry - Circles, Arcs, and Sectors
Repeated question (from previous section), there are 2 ways to talk about the 'size' of an arc. What are they?
2) Arc length
Of the 2 ways to talk about arc 'size', what would be the motivation to choose on over another aka when do you use arc measure to talk about arc size and when do you use arc length ?
When comparing arcs within the same circle, arc measure is fine.
Comparing arcs between different circles, arc measure is not enough and we use arc length .
How do we find the length of an arc?
For degrees its:
arc measure (in degrees) / total degrees in a circle, 360
That proportion must also be true for length:
length of arc / total length of circle (which is the circumference).
So once we know the proportion, we can apply that to the part we want to find out.
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Can we divide the whole area of a circle into fractions?
What is a circular sector?
How do we find the area of a circular sector?
From here we can do the same but instead of using the circumference we use the area as the denominator.:
Proportion
angle/360
must be equal to:
area of sector/ area of circle
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