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 2004-03-30 06:14:27