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 \(k\).

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