I am a student and need help answering this question on sectors. Please may I have a step by step solution.
The area of the major sector is $180cm^2$.
Calculate the perimeter of the major sector. Give your answer to 1 decimal place.
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Thank you and help is appreciated
The angle inside the sector is $360^\circ-120^\circ=240^\circ$. The area of a sector of a circle with angle $\theta$ is given by $$A=\frac{\pi r^2\theta^\circ}{360^\circ}$$
So knowing that this is $180$cm, we can work out what $r$ is. I get $r\approx9cm$, you can work out the exact value for your calculations (you'll probably need more precision).
Next you can use this to work out the perimeter. The perimeter of a sector of a circle with angle $\theta$ is given by $$P=\frac{2\pi r\theta^\circ}{360^\circ}$$ Using this, we can work out $P\approx36cm$. Finally add on the two lines connecting the sector together, each of length $r$, giving an answer of $\approx54cm$ (I suspect my rounding has caused significant errors though - you can use the machinery to get the correct answer).