geometry - What are the weights of the bangles?

John the jeweler is planning to make bangles from solid 14 karat gold. As shown below, his design will:

• be available in 5 different diameters (D)



• have a height (h) of 1 inch for all bangles


• have an inside profile that is straight


• have an outside profile with a radius of curvature (r) equal to D/2

John has fabricated a size XS prototype and found that it weighs 120 grams. John knows the density of 14 karat gold is 14 grams/cc, but is not sure how to calculate the weights of the other four bangles. He needs this information to determine the fabrication costs.

Can you help John by providing the weights of the other bangles with larger diameters?

^{This may look like a math textbook problem, however it is a variation of a classic geometry puzzle.}

Answer

They are exacty the same so also 120 gram.

By making the diameter bigger you also make the ring narrower. And these cancel eachother out.

A better explanation here