Watches are so much fun
Geometry
Level
2
The minute hand of a watch is \(x\) times bigger than its hour hand. Let the area swept by the minute hand be \(S_{m}\) and the area swept by the hour hand be \(S_{h}\). Knowing the watch is perfectly adjusted and considering a fixed interval of time, the quotient of \(\dfrac{S_{m}}{S_{h}}\) can be written as \(kx^{2}\). Find \(k\).
by
Eduardo Petry