Question

The length of an arc of a circle is 12cm. The corresponding sector area is 108cm^2. find the radius of the circle?

Answer 1

Let A the area, R the radius, a the angle in radian and L the length of the arc.

Then A = 1/2 a R² = 108 and L = a R = 12

a R² = 216 and a R = 12 thus R = 216/12 = 18 cm
the angle is a = 12/18 = 2/3 rad

Answer 2

rad* radius

Answer 3

I dont undertand.

Answer 4

could you try and dumb down your answer for me?

Answer 5

ok lets try this and see if it works

Answer 6

arc lenght you have is 12, and in general the arc length \(L\) given the angle \(\theta\) and the radius \(r\) is \(L=\theta r\)
in your case you know \(12=\theta r\)

Answer 7

the area \(A\) is 108 and in general the area given \(\theta\) and \(r\) is \(A=\frac{1}{2}\theta r^2\)
so you also know that \(108=\frac{1}{2}\theta r ^2\) or \(216=\theta r^2\)

Answer 8

so we have two equations,
\[ 216=\theta r^2\] and
\[12=\theta r\]

ok i stopped

Answer 9

i was using \(\theta\) in terms of radians, but it makes no difference for your problem because you are not looking for \(\theta\) just \(r\)

Answer 10

divide and you get \[\frac{216}{12}=\frac{\theta r^2}{\theta r}=r\]

Answer 11

cool.

Answer 12

The thing is that you are using information that you already know to solve this but you just need to mess around with it.

Answer 13

For example the area of a circle is pi * r^2
It can also rewrite it as 2* pi /2 * r^2
Where 2 * pi is 360 degrees or the full circle. But now we want the area of part of the circle so by knowing the degrees of the arc you can find a fraciton of it.

For example if you wanted an arc that represents half of the circle it will be half of 360 or half of 2 * pi = pi

so the area will be 1/2 * pi * r^2