If two sectors have an area of 12π square units, and one sector is from a circle with radius 6 units, while the other is from a
circle with a radius of 4 units, how do the central angles for these sectors compare?
2 answers:
Answer:
4 : 9
Step-by-step explanation:
Given:
Two sectors, each has an area of 12pi, but with radii r1=6 and r2=4 units.
Find ratio of central angles.
Solution:
Let A = central angle
Area of a sector = pi r^2 (A/360)
Since both sectors have the same area,
pi r1^2 (A1/360) = pi r2^2 (A2/360)
simplifying
A1 r1^2 = A2 r2^2
Therefore
A1 : A2 = r2^2 : r1^2 = 4^2 : 6^2 = 4 : 9
Answer:
Thus, the ratio of the central angles is 4 : 9.
Step-by-step explanation:
Area, A = 12 π square units
radius, R = 6 units
radius, r = 4 units
Area of sector is given by
For first sector
For second sector
So, the ratio is
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