Archimedes' problem was to determine whether a crown given to him by the king was made entirely of gold, or if it contained some other metal. This problem is significant because it showcases Archimedes' brilliant use of geometric principles to solve a real-world problem, and also demonstrates the importance of accurate measurement and the concept of density.
Archimedes used his famous "Eureka!" moment to solve the problem. He realized that he could determine the volume of the crown by measuring the amount of water it displaced when submerged. He then compared this volume to the volume of a solid gold object with the same weight. If the volume of the crown was larger, it meant that it contained some other metal with a lower density.
Yes, Archimedes' method worked. He discovered that the crown was indeed not made entirely of gold, as it had a lower density than pure gold. He was able to determine the exact amount of gold and other metals in the crown by using his method.
Archimedes' solution to this problem was significant because it was a breakthrough in the understanding of density and how it can be used to determine the purity of a substance. It also demonstrated the power and practical applications of mathematics in real-world problems.
Archimedes' solution has had a significant impact on modern science, especially in the field of physics. His principle of displacement and his method for determining density have been used in various experiments and calculations. His problem-solving approach and innovative thinking have also influenced scientists and mathematicians throughout history.