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Suppose the height is 15x cm.

Then the width is 8x cm.

Then the surface area is 2*(15x*8x + 8x*22 + 22*15x) cm2

Therefore 2*(15x*8x + 8x*22 + 22*15x) = 2506

or 15x*8x + 8x*22 + 22*15x = 1253

120x2 + 506x - 1253 = 0

so that x = -529/30 or 13/4

But x cannot be negative so x = 1.75.

Therefore, volume = (15*1.75)*(8*1.75)*22 = 8085 cm3

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