Finding the Radius of a Sphere

Date: 10/28/96 at 22:1:53
From: The Harpers
Subject: Radius of a Sphere

If I have a basketball and I want to figure out its volume and I don't 
know the radius (which is obviously very important in figuring out 
volume), how can I determine the radius?  Would the basketball's 
circumference lead me to the answer? 

Thanks,
   Holly

Date: Monday, October 28, 1996 4:36 PM
From: Doctor Daniel
Subject: Re: Radius of a Sphere
 
Hi Holly,

If we don't know anything about the sphere, like its surface area, its 
volume, how many marbles fit inside it, or something like that, we're 
not going to be able to compute its radius.  But if we do have that 
piece of information, we can solve for the radius using a function 
that contains both the radius and the information that we know.  

For example, since the formula for the volume is V = 4/3 pi r^3, we 
can solve this for the radius and get r = cuberoot (3 V / (4 pi)).  

Maybe this answers your question?

 Good luck,
 
 -Doctor Daniel,  The Math Forum
  Check out our web site!  http://mathforum.org/dr.math/   

Date: Monday, October 28, 1996 4:36 PM
From: Dr. Donald
Subject: Re: Radius of a Sphere

You have it exactly right. If you could figure out the circumference, 
which is 2 pi r, you could calculate the radius.  If the circumference 
is 27 inches, for instance, the radius would be 

  2 pi r = 27, 
       r = 27/2pi

Personally, I would go for measuring the diameter.  Rest the 
basketball on the floor against a flat door.  Take a large, hardcover 
book, put the spine of the book against the door so that the book is 
perpendicular to the door, slide the book down until the bottom of the 
book touches the top of the basketball, and then measure the distance 
from the bottom of book to the floor.  This will be a pretty accurate 
measurement of the diameter.  The radius is half of the diameter.  
Circumference is tough to measure, though if it is an OFFICIAL 
basketball, the circumference may be a specification of the ball.  I 
know that they measure baseballs by their circumference.

-Doctor Donald,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/