# Math Help - Compose area formula from image

1. ## 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?

Someone 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:

Tom Koolen

2. ## 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?

3. ## 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.

4. ## 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