Question

Find the area A of the sector of a circle of radius 90 in formed by central angle 1/6 radian.

Answer 1

Answer:

2121 $in^{2}$ Rounded to the nearest inch.

Step-by-step explanation:

A = $\pi r^{2}$  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 = $\frac{\frac{\pi }{6} }{2\pi }$ $\pi r^{2}$  The $\frac{\pi }{6}$ is the part of the circle and the whole circle is 2$\pi$

$\frac{\frac{\pi }{6} }{2\pi }$ is the same as $\frac{\pi }{6}$÷$\frac{2\pi }{1}$ Which is the same as $\frac{\pi }{6}$ x $\frac{1}{2\pi }$ Which is the same a $\frac{1}{12}$

A = $\frac{1}{12}$$\pi$$90^{2}$

A = $\frac{1}{12}$(3.14)(90)(90) = 2119.5.  When you use the $\pi$ on your calculator you get a slightly different number.  This is due to rounding.

A = 2120.575041