Diameter of a Ball

Date: 11/25/2001 at 22:55:18
From: Tabitha Howard
Subject: Physics

A child rolls a ball on a level floor 4.5m to another child. If the 
ball makes 15.0 revolutions, what is its diameter?

I don't know where to start.

Date: 11/26/2001 at 10:28:37
From: Doctor Ian
Subject: Re: Physics

Hi Tabitha,

Imagine that you paint a blue line around the widest part of the ball, 
and put a red dot at one point on this line. Then you roll the ball 
across the floor. You would see a pattern like this:

   -------*-------*---...---*-------*

where each '*' shows where the dot hit the floor, and each '-' shows 
where the blue line was hitting the floor. (We rolled the ball while 
the paint was still wet!)

Now, there will be one '*' for each time that the ball makes a 
revolution. So if the ball makes 15 revolutions, we'll see this:

  ---*---*---*---*---*---*---*---*---*---*---*---*---*---*---*

Each '---*' is the length of the blue line, which is to say, each 
'---*' is one circumference of the ball. So here's the situation:

  ---*---*---*---*---*---*---*---*---*---*---*---*---*---*---*
   c   c   c   c   c   c   c   c   c   c   c   c   c   c   c

  |----------------------------------------------------------|
                     4.5 meters

From this, we can find out what the circumference must be.  (15 
circumferences add up to 4.5 meters.) And from the circumference, we 
can find the diameter, using the formula

  circumference = pi * diameter

Can you take it from here?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/