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?
Thanks in advance.
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,
$\displaystyle Area\ of\ segment = \dfrac12 r^2 \theta$
for theta in radians and
$\displaystyle Area\ of\ segment = \pi r^2 \times \dfrac{\theta}{360^o}$
for theta in degrees.
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.