Cube Question In Space Geometry

[xenogizmo]

Hey everyone,
I came across this rather "uncoventional" space geometry question, from a dutch book. I have answers in mind but I want to check with you guys..
Check the attached picture for the cube..
The question goes like this:

This photograph of a cube was taken on a tropical island, so the sunbeams are directed almost perpendicular to the groud.

>In the pciture only part of the shadow is visible. What will the shadow look like "behind" the cube?

By changing the position of the cube or the sun, you can find different shapes of shadow. Assume the edge of the cube has length 1

>At which positions of sun and cube the shadow will be a square of 1 by 1?
>Describe a situation in which the shadow is a square with edges of length "root of 2" (approx. 1.4)

Now, I'll put my answers in the next post so that u can take your shot at the question first.

Thanks,
Xeno

 

[xenogizmo]

My Attempt..


Question 1: The shadow is a hexagon


Question 2: For the shadow to be 1x1, the sunbeams must be perpindular to one of the cube's faces

Question 3: The edge 1 was given for a reason I guess, (pardon me here, I'm not so familiar with the english terms) but I remember from back in school that if the edge length x then if we take a base of the cube, and draw a diagonal line from one edge to another, its length would be x by the root of 2 (I'm sure that line has a name, just don't know it)

So I guess the sunbeams must be perpindicular to one of hte edges of the cube, the one I marked with red in the picture attached to this post.

Tell if I'm right, and correct me if I'm wrong.
Thx

 

[xenogizmo]

No ideas yet?? :uhh: