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

Home > Shapes
Two ways up (Posted on 2002-05-05) Difficulty: 3 of 5
A tower, 200 feet high, has an elevator inside it, and a spiral stairway winding its way around the tower at a constant 30 degree angle with the horisontal.

Given the tower's radius of 10 feet, what is the difference between the distance covered by a person going up in the elevator, versus one climbing the stairs?

See The Solution Submitted by levik    
Rating: 2.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
xclent Q | Comment 11 of 14 |

Actually the stair case is going round and round .

forming an ellipse section with sides= a and b, major and minor axis.

a=10 b=?

cos30=base/2b. base=20. thus b=20 3 /3.

and hieght of this Traingle= 10 3 /3.

so this will go up by 200 / 10 3 /3 times i.e . 20 3 times.

now perimter of ellipse= pie*( a+b)

here in this case it is pie*(10+20  3 /3).

one side means half of it that is 5+10 3 /3.

so total distance will be: 5+10 3 /3  *  20  3 .

this will come as 200 + 100 3

so the difference will be 100 3.


  Posted by prashant on 2004-03-30 06:14:27
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (5)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information