Diameter = 10 inches
Radius = Diameter/2 = 10/2 = 5 inches.
Length of arc = [tex] \frac{Angle \: subtended \: by \: it}{360} \times 2πr[/tex]
Now,
Putting values,
[tex]10 = \frac{Angle \: subtended \: by \: it}{360} \times 2 \times \frac{22}{7} \times 5 \\ Angle \: subtended \: by \: it = \frac{10 \times 360}{2 \times \frac{22}{7} \times 5} \\ Angle \: subtended \: by \: it = \frac{360 \times 7}{22} [/tex]
Area of sector =
[tex] \frac{Angle \: subtended \: by \: it \: at \: centre}{360} \times π {r}^{2} \\ \frac{ \frac{360 \times 7}{22} }{360} \times \frac{22}{7} \times {5}^{2} \\ \frac{7}{22} \times \frac{22}{7} \times 25 \\ 25 \: {inches}^{2} [/tex]
Area of sector will be C. 25 inches².
