My boss set one empty can on its side on the floor, and one standing upright on top of a toolbox. The distance from the top of the side of the can on the floor to the top of the can on the toolbox measured 49 inches. When we turned the can on the tool box onto its side and stood up the can on the floor, the distance between the top of the can on the floor to the top of the can on the tool box was only 45 inches. Can anyone explain why this measurement changed?
In: 1
Pictures to help explain
The tape measure is overlapping the can on the toolbox, but the measure isn’t for the one on the ground since it starts on the top of the can. Since the measure includes the height of the can on the toolbox, but not the one on the ground, the can on the toolbox being upright will make the total distance longer.
In the simplest terms:
A cylinder basically connects two parallel surfaces or “bases” (two circles in the case of this can) at a fixed distance. The fixed distance is called the “height” of the cylinder, or the vertical part. The width of the two circles (also called the diameter) is also the width of the cylinder. That’s the horizontal part.
You keep the toolbox can standing up, you’re measuring the distance of the floor can from the top of the toolbox can, inclusive of the height of the toolbox can but not width/radius. You keep it lying down, you’re now measuring the distance from the top of the toolbox can to the floor can inclusive of width/radius of the toolbox can, but not the height.
Yeah, as odyssey explained, the difference is because the tape measure starts at different distances off the floor.
If we call the height of the toolbox top c, and assume the diameter of the can is 1 and the height is 2 (made up numbers):
First scenario (can on floor on its side is -1):
Measurement = 2 + C – 1 = 1+C
Second scenario (can on floor upright is -2):
Measurement= 1 + C – 2 = C – 1
The cans height and width are different, the one on the floor is subtracted from the total the one on top is added to the total distance, when you change orientation you change the total. If you lay them both on their side or have them both stood up you will get the same distance, which will be the same as the height of the tool box.
I will try to explain this like you are actually five.
When you have something that doesn’t make sense break it into pieces until it gets easy. Measure the bottom can to the top of the tool box standing up and laying down. Then measure the can on the tool box standing up and laying down from the floor.
Bottom can sideways= longer measurement
Bottom can upright= shorter
Top can sideways=shorter
Top can upright=longer
You are moving where the tape measure starts and the size of what you are measuring.
The tape measurer is telling you how far apart the two distances are (from the top of the toolbox can to the top of the floor can). Basically, top height minus bottom height.
When you raise the top height (put the toolbox can up) and lower the bottom height (put the floor can down), the difference in height gets bigger.
When you lower the top height (put the toolbox can on its side) and raise the bottom height (put the floor can up), the difference in height gets smaller.
Hope that helps.
Ye first measurement is cabinet height (C) minus can width (W) plus can height (H). C-W+H
The second is C-H+W.
C-W+H and C-H+W are two different things, so you expect them to add up to a different value.
I think it’s possible to explain this without actually doing math as some other responses have done. Let’s break down the differences between the two situations you’re measuring.
Start with your second picture. Now slowly tip the top can onto its side. Clearly you’ve reduced the distance, because you’ve lowered the top of what you’re measuring to be closer to the bottom.
Next, slowly stand the bottom can upright, to match your final picture. Again, you’ve reduced the distance, because now you’ve raised the bottom of what you’re measuring closer to the top.
In both steps you’ve reduced the distance, so it should not be surprising that the final distance is less than the initial distance.
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