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?
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 20040330 06:14:27 