Moving a refrigerator word problem

Question

A box containing a refrigerator is 3 ft wide, 3ft deep, and 6ft high. To move it, Wally lays it on its side, then on its top, then on its other side, and finally stands it upright. Exactly how far has point A traveled (if it starts in the top left corner and ends in the top left corner) in going from its initial location to its final location?

Answer 1

Mituku's response is appropriate if you are only concerned about horizontal movement, or the actual distance along the ground, and that would be the 18 feet.  If the question really wants to know everywhere A travelled, one needs to think a bit more creatively.  Each rotation of the box would cause the point to move in the arc of a circle.  Those individual arcs would need to be added together to compute the actual distance travelled.  

 

I initially used right triangle hypotenuses, but then realized it had to be arcs of circles.  Here's what I got for each rotation, which are all 1/4 circles with varying radii, so 1/4 of the circumference using 2(pi)r

 

1. First rotation, the circle has a radius of root 45, so the distance there is root(45)pi/2
2. Second rotation the circle has a radius of 3, so the distance is 3pi/2
3. Third rotation A is the pivot, so no movement of A
4. Fourth rotation, the radius is 6, so the distance is 3pi

 

Adding these pieces together gets (3root(5)pi+9pi)/2, or approximately 24.67 ft.  Interesting problem if you keep thinking about it.

Answer 2

Hi again Brie,

 

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The last 3ft count as move. It's not being pedantic to count it. It is just doing it the logical/right way. So the answer is 18.

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Assuming Wally moved the refrigerator on a straight path, if you draw it out that way, you will find that the distance between where the fridge was and where it ended up is 

 

6 + 3 + 6 = 15ft

 

But, if you would rather be pedantic about it, you can see that an additional 3ft from where they were and that would make the total 18ft.

 

I hope this helps