The area of the sector formed if the central angle of 2 radians cuts off an arc of length 4 inches is approximately 4 inches
The formula for calculating the length of an arc is expressed as:
[tex]L=\frac{\theta}{360} \times 2\pi r\\4 = \frac{114.6}{360} \times 2\pi r\\4=0.3183 \times 6.284r\\4=2.0001972r\\r=\frac{4}{2.0001972}\\r= 1.9998\\r \approx2in[/tex]
Get the area of the sector formed using the formula:
[tex]A_s = \frac{\theta}{360} \times \pi r^2\\A_s = \frac{114.6}{360} \times 3.142 (2)^2\\A_s = 0.3183 \times 3.142 \times 4\\A_s = 4.0003944 inches[/tex]
Hence the area of the sector formed is approximately 4 inches
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