Think about it. The two points that are furthest apart are the diagonal corners between the top and bottom. Call th width w, then the depth is also w (since it's square) and the height is 2w. Then
9 = √(w² + w² + (2w)²) = √(6w²) and
81 = 6w²
w² = 13.5 and
w = 3.674
Now, the 'ends' are w² (or 13.5) and there are 2 of them. And the 4 'sides' are 2w*w = 2w² = 27 and there are 4 of them. So the total area is
A = 4*27 + 2*13.5 = 135 cm²
HTH
Doug
2007-04-28 09:06:10
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answer #1
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answered by doug_donaghue 7
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Call the sides of the box x, x and 2x. We are told that the greatest distance between two points of the box is 9 cm. This distance will therefore be the diagonal of the box. Applying Pythagoras in 3D we have
x^2 + x^2 +(2x)^2 = 9^2
6x^2 = 81
x = 3sqrt(3/2) (4 dp) (Ignoring the negative solution)
Thus the surface area is
2 x (3sqrt(3/2))^2 + 4 x 6sqrt(3/2) x 3sqrt(3/2) = 135 cm^2
2007-04-28 16:08:31
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answer #2
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answered by aepacino 2
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The greatest will refer to the diagonal from the top left corner of the box to the bottom right corner.
Let x be the length of the base of the box, so its height is 2x.
Let d be the diagonal of the base.
d^2 = x^2 + x^2
d^2 = 2x^2
As the greatest distance is 9cm,
9^2 = d^2 + (2x)^2
81 = 2x^2 + 4x^2
81 = 6x^2
x^2 = 13.5
Total surface area
= 2(x^2) + 4(2x^2)
= 2x^2 + 8x^2
= 10x^2
= 10(13.5)
= 135 cm2
2007-04-28 23:20:22
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answer #3
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answered by Kemmy 6
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The greatest distance is the diagonal D that goes from the top left front vertex to the bottom right back vertex (or equivalent).
Draw a sketch.
The edges of the box are a, a and 2a.
You will notice that the diagonal of the box is a hypotenuse of a right triangle formed by the diagonal d of the base of the box, and by the height h of the box.
d = sqrt(2a)
h = 2a
=> D² = sqrt(2a)² + (2a)²
9² = 2a² + 4a²
6a² = 81
a² = 81/6
a² = 27/2
The total surface area is then
A = 2a² + 4(a·2a)
A = 10a²
(a² = 27/2)
A = 270/2
A = 135 cm²
Hope this helps.
2007-04-28 16:00:15
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answer #4
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answered by M 6
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Let x be the horizontal dimensions: so the height is 2x. Using Pythagoras's theorem in three dimensions:
x² + x² + (2x)² = 9²
Take it from there.
2007-04-28 16:05:28
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answer #5
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answered by Anonymous
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multiply the 9cm widest point by half of that which would be 4.5 cm that should be the total surface area
9x4
2007-04-28 16:03:53
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answer #6
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answered by applesjackk 3
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Sorry, I read this and don't have enough information to give an answer.
2007-04-28 16:00:17
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answer #7
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answered by Steven W 3
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Do your own home work.
2007-04-28 16:02:01
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answer #8
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answered by taxed till i die,and then some. 7
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135CM^
2007-04-29 10:30:29
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answer #9
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answered by Anonymous
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