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Quiz of the Month (October 2003)

Hector C. Parr

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SOLUTION TO LAST MONTH'S QUIZ

    1.  26.18 sq.cm
    2.  21.54 sq.cm
    3.  21.65 sq.cm
Notes 


 1.  r = 5 tan 30o
     So A = PI r2 = 26.179939


 
 2.  If side of square = x then
       x tan 30o + x/2 = 5
     So x = 4.6410162 and x2 = 21.539031




 3.  If b = base and h = height then
       h = (5 - b/2) tan 60o
     So Area = bh = (5b - b2/2) tan 60o

     Completing the square, 5b - b2/2
       achieves maximum value when b = 5.
     Then Area = 12.5 tan 60o = 21.650635

THIS MONTH'S QUIZ

1. Find the length of side of the smallest closed cubical box which can contain two snooker balls, each of diameter 2 inches.

2. Three snooker balls, each of diameter 2 inches, rest on a horizontal table. Each ball touches the other two, and a fourth similar ball rests on top, touching each of the first three. Find the height of the pile.

3. Fifteen snooker balls, each of diameter 2 inches, are held together on the table by a rack in the form of an equilateral triangle. On top of these rests a second layer of ten balls, each touching three balls of the first layer. A third layer of six balls rests on top similarly, followed by a fourth layer of three balls, and a single ball is placed on top to complete the pyramid. Find the height of the pyramid.

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(c) Hector C. Parr (2003)

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