Finding the the radius of a circle using S=Ør

[lanieley]

Finding the the radius of a circle using S=Ør

A wheel rolls 4? metres while rotating 120°.
Find the area of this wheel in square metres.
Give your answer as an exact value.

So far I think I need to use the formula S=Ør but I'm not sure which values correspond with the central angle (Ø) and S.
Any suggestions?

 

[Mrspi]

Re: Finding the the radius of a circle using S=Ør

A wheel rolls 4? metres while rotating 120°.
Find the area of this wheel in square metres.
Give your answer as an exact value.

So far I think I need to use the formula S=Ør but I'm not sure which values correspond with the central angle (Ø) and S.
Any suggestions?

theta is the angle...120 degrees, but you'll have to convert to radians.

4 pi is the arc length, or S.

When you substitute those into the formula, you should be able to find the value of r. Then, you can use the formula for the area of a circle.

 

[pka]

Re: Finding the the radius of a circle using S=Ør

Think in terms of radian measure. The central angle of one radian underlies an are of length equal to the radius of the circle. Now \(\displaystyle 120^ \circ \approx \frac{{2\pi }}{3}\) that is one-third of the whole. Now you are told that the wheel rolls 4m, that is the arc length.

 

[lanieley]

Re: Finding the the radius of a circle using S=Ør

Thanks a lot!
I think I've got it now.
Radius of 6 and an area of 36 pi metres squared.

 

[Deleted member 4993]

Re: Finding the the radius of a circle using S=Ør

Correct!!