The formula for the area of a sector of a circle is:
[tex]A=\frac{\theta}{360}\cdot\pi r^2[/tex]Where
θ is the angle
r is the radius
Given,
θ = 100
r = 7
We substitute into the formula and figure the answer out [remembering to use 3.14159 as π]:
[tex]\begin{gathered} A=\frac{\theta}{360}\cdot\pi r^2 \\ A=\frac{100}{360}\cdot(3.14159)(7)^2 \\ A=\frac{5}{18}\cdot(3.14159)(49) \\ A\approx42.76053 \end{gathered}[/tex]Rounding to the nearest thousandth [3 decimal places], we have:
Area = 42.761 square centimeters