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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... _________________
If You're Not Living On The Edge, You're Taking Up Too Much Space
Re: PS - Crystal Ball [#permalink]
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.