An ant starts from a point on the bottom edge of a right circular cylinder and moves in spiral manner along the curved surface area such that it reaches the top of cylinder at a point directly above the starting point in exactly 2 identical spirals. Find the distance covered by the ant if the radius of the cylinder is 6/pie
and height is 20 units.

• Just observe that horizontal distance travelled by the ant is 2 complete circles i.e. 2(2πr) = 24 units
  
  and vertical distance travelled is = height of the cylinder = 20 units.
  
  So the path covered by the ant = hypotenuse of the right angled triangle with legs of 24 and 20 units i.e. = √(24² + 20²) = √976 = 4√61.
• 11 years agoHelpfull: Yes(4) No(0)
• you can see spiral path is the diagonal distance that is traveled in single spiral so if we cut down the cylinder in two equal cylinders or half height and then further cut it down along the height to make them rectangular sheet then the diagonal of these two sheets is the total path traveled by the ant. so in this manner you can see the calculations below
  
  2*sqrt ((10)^2+(12)^2) =31.24 units .. and please see this image for better explanation i have tried to show how it works (not perfectly but a overview)
  click on this
  
  http://img534.imageshack.us/img534/9811/antwe.jpg
  
• 11 years agoHelpfull: Yes(2) No(2)