E-RA04 · Three adjacent sectors
Three adjacent, non-overlapping sectors of radius \(8\) cm have consecutive angles \(\theta\), \(\displaystyle \theta+\frac{\pi}{3}\) and \(2\theta\). The remaining gap around the centre is \(\displaystyle \frac{\pi}{6}\). The three sectors together form one connected region.
Find \(\theta\) and each of the three sector angles.
Find the total curved length and the total area of the three sectors.
Find the outside perimeter of the connected region. Explain why adding the three individual perimeters gives a different result.
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