$\cos (\theta/2) = 4.5/9$
$\theta = 120^\circ$
$\beta = 360^\circ - \alpha = 360^\circ - 120^\circ$
$\beta = 360^\circ - 120^\circ$
$\beta = 240^\circ$
$A_1 = \frac{1}{2}r^2 (\theta_{rad} - \sin \theta_{deg})$
$A_1 = \frac{1}{2}(9^2) \left[ 120^\circ \left( \dfrac{\pi}{180^\circ} \right) - \sin 120^\circ \right]$
$A_1 = 49.749 \, \text{ m}^2$
$\text{Common area} = 2A_1 = 2(49.749)$
$\text{Common area} = 99.498 \, \text{ m}^2$ Part 1: [ D ]
$\text{Area of water surface} = 2(\pi r^2 – A_1)$
$\text{Area of water surface} = 2[ \, \pi(9^2) – 49.749 \, ]$
$\text{Area of water surface} = 409.44 \, \text{ m}^2$ Part 2: [ A ]
$\text{Perimeter} = 2 \times \dfrac{\pi r \beta_{deg}}{180^\circ} = 2 \times \dfrac{\pi(9)(240^\circ)}{180^\circ}$
$\text{Perimeter} = 75.398 \, \text{ m}$ Part 3: [ B ]
