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

• Jan 25th 2011, 10:49 AM
MathIsCool12
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?

• Jan 25th 2011, 10:57 AM
Unknown008
Arc length = $r\theta$

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

Otherwise,

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

for theta in degrees.

Similarly,

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

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

for theta in degrees.
• Jan 25th 2011, 11:08 AM
MathIsCool12
That is brilliant thank you very much. another question, what formula do i use? how do i decide between radians and degrees?
• Jan 25th 2011, 11:18 AM
Unknown008
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.
• Jan 25th 2011, 03:27 PM
MathIsCool12
thats brilliant, thank you for your help.