A rectangular sheet of tin 44 cm by 33 cm is curled round until its two 33 cm edges meet, so the 44 cm edge becomes the circumference of a cylinder. An identical sheet is curled the other way, its 44 cm edges meeting, so the 33 cm edge becomes the circumference. Find the ratio of the volume of the first cylinder to that of the second. Take π = 22/7.

First cylinder: 2π$r=44$ gives $r=7$ cm and the height is 33 cm, so its volume = $(22/7)\times 49\times 33=5082{\text{cm}}^3$. Second: 2π$r=33$ gives $r=5.25$ cm and the height is 44 cm, so its volume = $(22/7)\times 27.5625\times 44=3811.5{\text{cm}}^3$. Ratio = 5082 : 3811.5 = 4 : 3 — the same as the ratio of the sheet's sides, because the volume works out proportional to $(circumference{)}^2$ × height. (Answering 1 : 1 assumes two identical sheets must hold the same amount, but the radius is squared while the height is not, so the short fat roll always wins; 3 : 4 turns the answer over; 16 : 9 squares the side ratio once too often.)