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Question
The area of the sector of a circle of radius 12 cm is 60π cm2. The central angle of this sector is ______.
Options
120°
6°
75°
150°
Solution
The area of the sector of a circle of radius 12 cm is 60π cm2. The central angle of this sector is 150°.
Explanation:
Area of sector = 60π cm2
Radius r = 12 cm
`"Area of sector" = θ/360xxpir^2`
`60pi = θ/360xxpixx12^2`
`60pi = θ/360xxpixx144`
`60 = θ/360xx12^2`
`60xx360/144=θ`
`θ= 150`
Thus, the central angle of this sector is 150°
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