Answer:
2121 [tex]in^{2}[/tex] Rounded to the nearest inch.
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex] Is the formula for a circle, but we only have a portion of a circle so we will have to adjust the formula for a part of the circle.
A = [tex]\frac{\frac{\pi }{6} }{2\pi }[/tex] [tex]\pi r^{2}[/tex] The [tex]\frac{\pi }{6}[/tex] is the part of the circle and the whole circle is 2[tex]\pi[/tex]
[tex]\frac{\frac{\pi }{6} }{2\pi }[/tex] is the same as [tex]\frac{\pi }{6}[/tex]÷[tex]\frac{2\pi }{1}[/tex] Which is the same as [tex]\frac{\pi }{6}[/tex] x [tex]\frac{1}{2\pi }[/tex] Which is the same a [tex]\frac{1}{12}[/tex]
A = [tex]\frac{1}{12}[/tex][tex]\pi[/tex][tex]90^{2}[/tex]
A = [tex]\frac{1}{12}[/tex](3.14)(90)(90) = 2119.5. When you use the [tex]\pi[/tex] on your calculator you get a slightly different number. This is due to rounding.
A = 2120.575041
