A circular cylindrical post with a circumference of 4 feet has a string wrapped around it, spiraling from the bottom of the post to the top of the post. The string evenly loops around the post exactly four full times, starting at the bottom edge and finishing at the top edge. The height of the post is 12 feet. What is the length, in feet, of the string?

Thanks!

AnonymousConfusedGuy
May 17, 2018

#1**+1 **

This seems to be harder than it really is......

Notice that if we "unwrapped" one complete revolution of the string around the post, we would have a rectangle with a "width" of 4 ft [the circumference of the post ].....and the height of this rectangle would be just 12 / 4 = 3ft

And the string would run from the top left of this rectangle to the bottom right, thus comprising the diagonal of this rectangle .......so....the length of this string would be the hypotenuse of a right triangle with legs of 3 and 4.....and its length = sqrt [3^2 + 4^2] = sqrt [ 25] = 5

And we have 3 more similar rectangles in the next 3 revolutions.....so....the string length is just

1 revolution * 5 ft + 3 revoultions * 5 ft =

4 * 5 ft =

20 ft

CPhill
May 17, 2018