Monday, September 6, 2010

September 6. 2010 (Labour Day)

We met last two weeks, and did problems from the book "Learning Maths 6B by Norrin Hasim (Singapore Asian Publications)". I highly recommend this book for middle school kids for a variety of very nice problems - I haven't seen other levels of this book - but 6B has lots of nice geometric problems. Today's Problems 1-3 are based on this.
  1. Find the area of the American Football in the square of side 45 cm long, in the above picture.
  2. 1/5th of Anant's mm's are same as that of 1/3rd of Aditya's. If Aditya gives Anant 24 mm's (unlikely though!), Anant will have thrice as many mm's as Aditya. How many they had to begin with?
  3. A solid iron ball of volume 576 cubic-centimeter is cast into nine identical solid cubes.  What are the dimensions of the cube?
  4. What about the other way around? Suppose you have 16 identical cubes, each having a side length  of 2cm long, is cast as a solid ball. What is its radius?
  5. A string forms an equilateral triangle, whose sides are 3.14cms long. The same string is now reshaped as a circular ring. What is the radius of the ring? 
  6. A circular race track has a inner radius of 56m and outside radius of 63m. What is the total area of the track itself?
  7. In the above problem, if the 7mts wide track is divided into 7 equally spaced ones- 1mts each, 7 racers need to run the full length of the track once - how should you place them so that each of them cover the same length? 
  8. The difference between the ages of Mr. Young and Ms. Old is 45 years and the ratio of their ages is 3:8. What are the ages of Mr. Young and Ms. Old.
  9. Divide 25 into two parts, such that 4 times of one part is the same as 6 times the second. 
  10. In a large movie hall, seats are assigned with respect to row and column numbers. In all there are 1296 seats, and the number of rows are the same as columns - how many rows are there?

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