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A closed rectangular box is a "double cube", in which the top and bottom are squares, and the height is twice the width. The greatest distance between any two points of this box is 9cm. What is the total surface area of the box?

2007-04-28 08:56:23 · 9 answers · asked by Unknown! 2 in Science & Mathematics Mathematics

9 answers

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 · answer #1 · answered by doug_donaghue 7 · 2 5

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 · answer #2 · answered by aepacino 2 · 0 0

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 · answer #3 · answered by Kemmy 6 · 0 0

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 · answer #4 · answered by M 6 · 6 0

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 · answer #5 · answered by Anonymous · 0 0

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 · answer #6 · answered by applesjackk 3 · 0 3

Sorry, I read this and don't have enough information to give an answer.

2007-04-28 16:00:17 · answer #7 · answered by Steven W 3 · 0 3

Do your own home work.

2007-04-28 16:02:01 · answer #8 · answered by taxed till i die,and then some. 7 · 0 3

135CM^

2007-04-29 10:30:29 · answer #9 · answered by Anonymous · 0 0

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