Monday, January 22, 2007
Circular stairway puzzle
Hi,
Having a good brain and uses it.
Once upon a time there was a very big poly sided gas tank in Singapore, somewhere in the Kallang basin area. It was said that it could hold one million cubic metres of gas. Big tanks like that had to be maintained, and maintenance people had to climb up to the top by means of a vertical steel ladder. Climbing such a ladder was hazardous, so a peripheral stairway resembling a circular staircase around the tank was built instead. This was safer, allowing for rest, and not so tiring to climb.
There is another type of tank somewhat like that. It has a circular stairway which wounds around it exactly four times, such that the top of the stairway is directly above the bottom of the stairway.
An enthusiast wanted to find out the length of this stairway. Using instruments he calculated that the tank was 96 feet high and has a circumference of 78 feet. Having done that he sat down and did some more calculation, and then he declared that he had the answer.
Well, was he a genius, some wizard with special powers, or, has he really a way to determine it simply like that ? Or he was just smart ?
Have a nice day
Ronald
The answer:
The length of the inner side of the stairway is approximately 326.5 feet.
The method:
View the tank as if it was two dimensional, split at a vertical line from the top of the stairway to its bottom. Thus, the view was four rectangles, with the hypotenuse being the stairway; and the answer was plain Mathematics using Pythagoras theorem.
Length = 4 x sq.root of (24 x 24 plus 78 x 78).
The lesson:
There are different ways to look at a problem.
Having a good brain and uses it.
Once upon a time there was a very big poly sided gas tank in Singapore, somewhere in the Kallang basin area. It was said that it could hold one million cubic metres of gas. Big tanks like that had to be maintained, and maintenance people had to climb up to the top by means of a vertical steel ladder. Climbing such a ladder was hazardous, so a peripheral stairway resembling a circular staircase around the tank was built instead. This was safer, allowing for rest, and not so tiring to climb.
There is another type of tank somewhat like that. It has a circular stairway which wounds around it exactly four times, such that the top of the stairway is directly above the bottom of the stairway.
An enthusiast wanted to find out the length of this stairway. Using instruments he calculated that the tank was 96 feet high and has a circumference of 78 feet. Having done that he sat down and did some more calculation, and then he declared that he had the answer.
Well, was he a genius, some wizard with special powers, or, has he really a way to determine it simply like that ? Or he was just smart ?
Have a nice day
Ronald
The answer:
The length of the inner side of the stairway is approximately 326.5 feet.
The method:
View the tank as if it was two dimensional, split at a vertical line from the top of the stairway to its bottom. Thus, the view was four rectangles, with the hypotenuse being the stairway; and the answer was plain Mathematics using Pythagoras theorem.
Length = 4 x sq.root of (24 x 24 plus 78 x 78).
The lesson:
There are different ways to look at a problem.
# posted by chunmu @ 5:41 PM 
