Question

An Arc length 3 feet is cut off by a central angle of pi/4 raidians, find the area of the sector formed

Answer 1

Could you help me please?

Answer 2

Probably not the quickest solution, but:
since the arc is cut off by an angle of pi/4, it means it's 1/8th of the whole circle. It means the whole circle measures 3*8 = 24 = 2pi*R , where R is the radius of said circle, which measures 24/2pi.
The surface of the whole circle is pi*R^2, replacing: \[\pi* ({24\over2\pi})^2 = 144\pi\]. Since you don't need the whole circle, but just 1/8th of it you get that your sector has a surface of 18pi.

Answer 3

So the final answer is 18 pi?

Answer 4

Apparently :) double check calculations to be sure, but the reasoning behind them works.

Answer 5

Thanks :)