Isaac Physics - King Hiero's Crown

King Hiero II hired a goldsmith to make him a gold crown. Yet, he has a feeling that the goldsmith had cheated him and alloyed the crown with silver whilst keeping some of the unused gold for himself. He asks the Greek mathematician Archimedes of Syracuse to find out if the crown is in fact pure gold without spoiling the crown.

Throughout this question, assume that the density of gold is 19.32gcm −3 and the density of silver is 10.49gcm −3.
Part A) The (small) 'gold' crown, weighing 900g, is placed into a cylindrical container of radius 5.00cm.

By how much would the water level rise if the crown was pure gold?
I got 0.593 which was correct.
But Part B
Given that the water level instead rises by 0.772cm, what percentage of the crown by mass is alloyed with silver?
I got 50.7% which is apparently incorrect but i'm not sure how...
Any help would be lovely!

(edited 1 year ago)

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