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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Watches are so much fun

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.