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Sagot :
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
[tex]A=\frac{\theta }{360}\times \pi r^{2}[/tex]
For first sector
[tex]12\pi=\frac{\theta }{360}\times \pi \times 6^{2}\\\\\theta = 120^{o}[/tex]
For second sector
[tex]12\pi=\frac{\theta' }{360}\times \pi \times 4^{2}\\\\\theta' = 270^{o}[/tex]
So, the ratio is
[tex]\frac{\theta}{\theta'}=\frac{120}{270} =4 : 9[/tex]
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
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