Expert: Ahmed Salami - 5/21/2004

Question
  When the snow stopped falling, Kelly, Miguel and Niha rushed outside to build a snow statue. Kelly made one large snowball for the head. Miguel made a larger snowball for the middle section. Niha made a giant snowball fro the bottome section.
  As they were getting ready to put the snow statue together, the children noticed that the circumference of the smallest section was about 2/3 the circumference of the middle section. The middle section was about ¾ the circumference of the largest section. When they measured the smallest snowball, they found it had a circumference of about 80 centimeters.

Question 1: How tall was the snow statue when the sections were piled one on top of the other?

Question 2: The group would like to make another snow statue with a total height of at least two meters. If all the other conditions are kept the same, what circumference will they need for the smallest section?


Answer
Hi,
I am sorry for the delay.
Alright, let the snowball sizes have circumferences x,y,z in ascending order.
From the question,
x = (2/3)y  implying y = (3/2)x
y = (3/4)z  implying z = (4/3)y = (4/3)(3/2)x = 2x
Let the diameters of the snowballs be a,b,c (these represents the height of each ball)
Then,
x = #a implying a = x/#
y = #b implying b = y/# = (3/2)(x/#)
z = #c implying c = z/# = 2x/#
where # represents pi - the ratio of circumference to diameter
Total height = x/# + 3x/2# + 2x/# = 9x/2#
but x = 80
Total height = (9)(80)/2# = 360/#
For the case where they should have a total height of at least 200 centimeters,
9x/2# >= 200
x >= 400#/9

Hope it is helpful.
You can always ask more.