The area of the sector which has a central angle of 5π/7 radians and a diameter of 5.6 in is 8.79 in².
The area of a circular sector is the total space occupied by it. The sector area is half of the product of the square of radius of the circle and the central angle.
It can be calculated as,
[tex]A_{sector}=\dfrac{d^2\theta}{8}[/tex]
Here, (d) is the diameter of the circle and (θ) is the central angle.
The central angle of the sector is 5π/7 radians and the diameter of the sector is 5.6 in.
Put the values in the above formula as,
[tex]A_{sector}=\dfrac{(5.6)^2\times5\pi}{8\times7}\\A_{sector}=\dfrac{(5.6)^2\times5\pi}{8\times7}\\A_{sector}=8.79 \rm \; in^2[/tex]
Hence, the area of the sector which has a central angle of 5π/7 radians and a diameter of 5.6 in is 8.79 in².
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