Sunday November 21, 2010

• A thick metal pipe,  2mts long, has inner radius of 12 cms and outer radius of 15cms, is made of steel. How much volume of steel is used to make this pipe?  What do you think is the weight of this pipe? Note that weight of 1 cubic meter of steel is 8000 Kg.  What if the pipe is made of Bamboo - 1 cubic meter of Bamboo is approximately 350 Kg.
• The new Chapman Mills park is rectangular, where the sides are in the ratio of 4:3. The total area of this park is approximately 3500 sq mts. What is the cost of installing a metal fence around this park, where The Ottawa Fencers charges approximately $45 per linear meter.
• Ms. Quick finishes a job in 8 days, whereas Mr. Slow finishes the same job in 12 days. How long will it take if both of them will work together (assuming that the job can be partitioned nicely (like pulling weeds in the garden)).
• Dr. Light needed to climb his wall to install the newly bought Christmas lights. His ladder is 8mts long, and the wall is approximately  7mts long. How far is the base of the ladder from the wall? Do you think its at a safe distance and will he be stable on the ladder?
• Suppose we toss two unbiased coins 100 times and observe that the number of times we get 2 heads is 25 and number of times we get no heads is 18. How many times we got at least 1 tails? We can try the same problem with 3 coins - lets say #times 3 heads= 22, #times 2 heads=32, #times 1 heads = 24, #times 0 heads = 22.   How many times we get at least one tails, at least one tails and one head.
• A disc needs to be cut out from a square sheet. The length of the sheet is 2mts. Whats the area of the largest possible disc? Whats the area of the left out piece of the sheet? Try the same problem for a cube and a sphere. Is the volume of the left out piece larger than that of the sphere?
• The angles of a triangle are in the ratio of 1:2:3. What are the angles?  Is it a right angle triangle? What if it is 3:4:5?
• Mr. Too Quick puts all his favorite NHL-team socks in the drawer, and in the morning rush (in the dark in long Northern Winter)  - what are chances that he will draw a pair which is of the same team. He has 2 pairs of SENS, 2 pairs of PENS, 2 pairs of  DUCKS and 3 pairs of HAWKS. What are the chances that he will draw a pair which does not belong to the same team?  First try this for two teams, and lets say one pair from each team, and then start to make it more complex.