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| For The Mathematically Inclined |
Anil Saigal
07/30/2008
FOR STUDENTS
PROBLEM # 1
A dart is thrown at a circular dart board of radius one. The dart can land at any place on the dartboard with equal probability. What is the mean distance between where the dart hits from the center of the board?
FOR GROWNUPS
PROBLEM # 2
Water flows into a tank at a rate of 1 gallon per second. Water leaves the tank at a rate of 1 gallon per second for each 100 gallons in the tank. The tank is initially empty. How long will it take for the tank to fill with 50 gallons of water?
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Problem Solutions 07/24/08PROBLEM # 1
What is the height of a pentagon with side length of 1?
Solution:
1.54.
FOR GROWNUPS
You have a circular piece of paper with radius 1 and wish to form a cone shaped cup. You may cut out any wedge you like from the paper, call the angle of the wedge x. The point of the wedge must be at the center of the circle. After cutting out the wedge you then attach the two straight edges remaining to form a cone. Assuming the paper cone can hold water, what should x be to maximize the water holding capacity of the cone?
Solution:
66.1 degrees.
Congratulations to Aseem Chandawarkar, Sitaram Chandawarkar, Manish Goregaokar, Shailesh Goregaonkar, Dattatraya Joshi and Prabhakar Nadkarni, who were winners of the last set of puzzles.
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