Geometry – Circles

Q: The radius of Circle M is twice as long as the radius of Circle N. What is the ratio of the area of Circle M to the area of Circle N?
 
Answer:  4:1 or 4/1. 
Explanation:  The ratio of the radii (2:1) is a length ratio. Square the length ratio to get the area ratio (4:1).  This works for all pairs of similar figures.
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Geometry – circles

Q: The area of a 45 degree sector of circle M is 100 square units. What is the area of circle M?

Answer: 800 square units

Explanation:  The 45° sector is exactly 1/8 of the circle. (45/360 = 1/8)

100 = 1/8 of the area of the whole circle.

The area of the whole circle is 800.

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