MathDB

4

Part of 2016 LMT

Problems(2)

2016 LMT Individual #4

Source:

4/10/2016
A triangle has two sides of lengths 19841984 and 20162016. Find the maximum possible area of the triangle.
Proposed by Nathan Ramesh
2016 LMT Theme #4

Source:

4/11/2016
A male volcano is in the shape of a hollow cone with the point side up, but with everything above a height of 6 meters removed. The resulting shape has a bottom radius of 10 meters and a top radius of 7 meters, with a height of 6 meters. He sat above his bay, watching all the couples play. His lava grew and grew until he was half full of lava. Then, he erupted, lowering the height of the lava to 2 meters. What fraction of the lava remained in the volcano?
Proposed by Matthew Weiss