# Thread: how to calculate the area and arc length of a given sector of a circle?

1. ## how to calculate the area and arc length of a given sector of a circle?

I need to calculate the area and arc length of a major sector of a 60mm diameter circle. the sector is 252 degrees. how do i do this?

2. Arc length = $\displaystyle r\theta$

where r is the radius and theta is the angle in radians.

Otherwise,

$\displaystyle Arc\ length = 2\pi r \times \dfrac{\theta}{360^o}$

for theta in degrees.

Similarly,

$\displaystyle Area\ of\ segment = \dfrac12 r^2 \theta$

$\displaystyle Area\ of\ segment = \pi r^2 \times \dfrac{\theta}{360^o}$

for theta in degrees.

3. That is brilliant thank you very much. another question, what formula do i use? how do i decide between radians and degrees?

4. Well, were you taught the formulae I gave you where theta is in radians?

Using those formulae is faster, but since you were given the angle in degrees, you better use that.

Also, you see how I got those formulae where theta is in degrees?

For the arc length, it is the circumference of a circle, multiplied by the angle divided by 360 degrees.
For the area, it is the area of a circle, multiplied by the angle divided by 360 degrees.

5. thats brilliant, thank you for your help.

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### how to calculate the area and the arc lenght of the sector

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