A copper wire of diameter 4 mm is wound closely, turn touching turn, round a cylinder 24 cm long and 20 cm in diameter, so as to cover its curved surface exactly once. Find the length of the wire in metres. Take π = 3.14.

Each turn uses up 4 mm = 0.4 cm of the cylinder's length, so the number of turns = 24/0.4 = 60. Every turn is one trip round the cylinder, of length π$d=3.14\times 20=62.8$ cm. Wire = $60\times 62.8=3768$ cm = 37.68 m. (Using the radius 10 cm in place of the diameter halves every turn and gives 18.84 m.)