Question

When BA=10ft, find the area of the region that is not shaded

Answer 1

I'm assume BA is the radius?

Answer 2

yeah

Answer 3

segment of a circle => \(\bf \cfrac{(\theta-sin(\theta)) r^2}{2}\)

Answer 4

darn... I got that in radians.

Answer 5

how do get the theta

Answer 6

one sec

Answer 7

\(\bf \cfrac{(\theta-sin(\theta)) r^2}{2}\\
\cfrac{(\frac{\pi}{3}-sin\left(\frac{\pi}{3}\right)) r^2}{2}
\implies \cfrac{\frac{100 \pi}{3}-100sin\left(\frac{\pi}{3}\right)}{2}\\
\cfrac{\frac{100 \pi}{3}-100\left(\frac{\sqrt{3}}{2}\right)}{2}
\implies
\cfrac{\frac{100 \pi}{3}-50\sqrt{3}}{2} \implies
\cfrac{\frac{100\pi -150\sqrt{3}}{3}}{2}\\
\cfrac{100\pi -150\sqrt{3}}{6}\)

Answer 8

since the equation uses radian, so I set 60 degrees to \(\bf \frac{\pi}{3}\) radians

Answer 9

so the area that is not shaded will be the circle's full area minus the segment's
\(\bf \pi r^2 -\cfrac{100\pi -150\sqrt{3}}{6}\)