Question

Find the area of the shaded regions:

QUICKLY!!!!!

Answer 1

`41.89\ cm^2`

Explanation:

`We\ are\ given:\\In\ two\ concentric\ circles,\\OD=3\ cm\\BC=4\ cm\\\angle DOB=\angle AOC=120\\Now,\\We\ know\ that:\\Area\ of\ a\ sector\ with\ a\ central\ angle\ \theta\ and\ a\ radius\ r\ is:\\A=(\theta)/(360)* \pi r^2\\Here,\\Area\ between\ the\ sectors=Area\ of\ Larger\ Sector - Area\ of\ smaller\ sector=(\theta)/(360)*\pi(R^2-r^2),\ where\ R\ and\ r\ are\ radii\ of\ the\ respective\ circles\ and\\ \theta\ is\ the\ common\ central\ angle.\\Here,\\R=4+3=7\ cm\\r=3\ cm\\ \theta=120\\ Hence,`

`Area\ of\ the\ shaded\ region=(120)/(360)*\pi(7^2-3^2)=(1)/(3)*\pi(49-9)=(1)/(3)*\pi(40) \approx 41.89\ cm^2`