Teaser 2912: Be crafty and box clever

From The Sunday Times, 15th July 2018 [link]

Tyson, a crafter, had several cylindrical enclosed boxes (with heights equal to diameters) in two sizes. Each box’s surface area (including top and bottom) was a three-figure integer in square centimetres, and the larger boxes had a radius which was a whole number multiple of that of the smaller boxes.

He kept them all in one vertical stack, to within one centimetre of the top of their metre-deep storage bin. Whilst working out fabric-cutting schemes, Tyson found that all the bigger boxes’ surface areas combined equalled all the smaller boxes’ surface areas combined and that the total surface area (in square centimetres) of all the boxes had all its numerals in ascending order.

What was the total surface area of all the boxes, in square centimetres?

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