The Constant Volume Of A Napkin Ring

Whether you drill through a tiny marble or a massive planet, the volume of the remaining ring depends only on its height. If the rings have the same height, they have the exact same volume regardless of the sphere's size.

This geometric mystery defies our intuition because we expect larger spheres to leave behind more material. Surprisingly, the extra volume added by the larger sphere's width is perfectly canceled out by the geometry of the hole. This means a ring made from a sphere the size of the Earth and one made from a ping pong ball are identical in volume if their height matches. It is a beautiful mathematical proof that highlights how size and shape interact in unexpected ways.