A circle of radius 9 cm is divided into three equal sectors.
Calculate
a) The length of the arc of each sector
\(\boxed{ \begin{array}{rcll} c&=&2\cdot\pi\cdot r \end{array} } \)
\(\begin{array}{rcll} \frac{c}{3}&=& \frac23 \cdot\pi\cdot r \\ \frac{c}{3}&=& \frac23 \cdot\pi\cdot 9\ \text{cm}\\ \frac{c}{3}&=& 6 \cdot\pi \ \text{cm} \qquad | \qquad \pi = 3.14159265359\dots\\ \frac{c}{3}&=& 18.8495559215 \ \text{cm}\\ \end{array} \)
b) the area of each sector
\(\boxed{ \begin{array}{rcll} A&=& \pi\cdot r^2 \end{array} } \)
\(\begin{array}{rcll} \frac{A}{3}&=& \frac{\pi}{3}\cdot r^2 \\ \frac{A}{3}&=& \frac{\pi}{3}\cdot 9^2 \ \text{cm}^2 \\ \frac{A}{3}&=& \frac{\pi}{3}\cdot 81\ \text{cm}^2\\ \frac{A}{3}&=& 27\cdot \pi \ \text{cm}^2 \qquad | \qquad \pi = 3.14159265359\dots\\ \frac{A}{3}&=& 84.8230016469\ \text{cm}^2\\ \end{array} \)
