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PS - Crystal Ball

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Director
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PS - Crystal Ball [#permalink] New post 25 Mar 2009, 12:12
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D
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A crystal ball is contained in a hexagon gift box. If the radius of the ball is 2inches, what is the minimum surface area of the box, in square inches? [Assume that thickness of the box could be negligible]
A 48*root3
B 40*root3
C 36*root3
D 24*root3
E 20*root3



I got 16*root3... :!:
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Director
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Re: PS - Crystal Ball [#permalink] New post 25 Mar 2009, 22:44
A? I got 48root3. what is OA?

circle is inscribed in a hexagon, draw a line from center of circle to one side of hexagon, its length is 2. so u get a 30-60-90 triangle. base of this triange is 2/root3. So the one side of hexagon is 2*(2/root3) = 4/root3.

now, to calculate area of the lid we divide into 6 equilateral triangles. We need to find the area of the one equilateral triangle and multiply by 6.

Area of our 30-60-90 triangle is 2/root3. so area of each equilateral triangle is 4/root3. Multiplying by 6 we get 8root3. Two lids = 16root3.

Each side is 4/root3 and height is 4. so total area of 6 sides is 4/root3*(4)(6) = 32root3.

hence, total area is lids + sides = 48root3.
Director
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Re: PS - Crystal Ball [#permalink] New post 26 Mar 2009, 09:41
Perfect....OA is A, I missed the second part. (I assumed thickness = width of box...shame!!)

thank you for nice explanation.
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Senior Manager
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Re: PS - Crystal Ball [#permalink] New post 26 Mar 2009, 11:58
Thanks for the explanation Economist.
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Re: PS - Crystal Ball   [#permalink] 26 Mar 2009, 11:58
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