All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
Perplexus Icon plus one (Posted on 2005-06-18) Difficulty: 2 of 5
A square table (a meter a side) has two spheres on its surface. The spheres have two special properties:

1. The larger is twice the diameter of the smaller, and
2. They are the largest size that will fit on the table without falling off. (They may extend over the edge of the table.)

I. What are the dimensions of the spheres?

II. A third sphere is added next to the other two. What is its largest possible size?

See The Solution Submitted by Leming    
Rating: 4.5000 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Great problem | Comment 5 of 12 |

Not terribly difficult, but very interesting results.

I liked it enough to make a picture.

http://www.mohawk.mtrsd.k12.ma.us/site/dept/math/jgalvagni/perplexpedestal.bmp

The central image is the top view showing the pedestal as a square, the 3 spheres and the points of tangency.

Each of the others is a projection perpendicular to the base of the pedestal and one of the lines connecting the centers of two spheres.
(The upper center is the solution for part I, the upper left and bottom together show part II, the upper right is just another projection)


  Posted by Jer on 2005-06-20 17:09:20
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information