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Compose area formula from image

Hello everyone,

The prelude to an optimalisation problem with areas is the composition of the area formula. However, I have come across an image from which I just cannot seem to create the formula, however I have got the feeling that it should be incredibly easy. Could someone please take a look?

Attachment 27687Someone places n of these boxes upon one another (n does not have to be an integer) to create a block with volume 1000.

Prove that the area formula is:

Attachment 27688

Thanks in advance,

Tom Koolen

Re: Compose area formula from image

Area formula for **what** area? The total observable surface area? Or the surface area that can be seen in your picture?

And what have **you** done on this? Have, you, for example, calculated what n must be?

Re: Compose area formula from image

The total observable surface area. And I have tried my best on this problem, but there is no work that I can show except for these two equations:

Area = n(10r^2+60r)

Volume = n(25r^2) = 1000

And I honestly have no clue as to what I have to do with two variables in this problem.

Re: Compose area formula from image

For the volume when n blocks are placed one above the other.

Volume V = area of base * height

= 5r^2 * 5n = 25r^2 n

For the lateral surface area = perimeter of the base * height

= 2 ( 5r + r ) * 5n= 60 r^2 n.

The area of the base and the top = 2 ( 5r *r) = 10r^2

Now you can proceed to solve the question