A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is $$v,$$  the total area around the fountain that gets wet is :

Solution :
Total area around fountain
$$\eqalign{ & A = \pi R_{\max }^2 = \pi \frac{{{v^4}}}{{{g^2}}} \cr & \left[ {\because {R_{\max }} = \frac{{{v^2}\sin 2\theta }}{g} = \frac{{{v^2}\sin {{90}^ \circ }}}{g} = \frac{{{v^2}}}{g}} \right] \cr} $$