A copper wire of diameter 6mm is evenly wrapped on the cylinder of length 18cm and diameter 49 cm to cover the whole surface. Find the length and volume of the wire.

The copper wire will form a tight spiral around the cylinder, but we can approximate to this by treating the wire as a number of segments. Each segment has a length equal to the circumference of the cylinder, which is 49π cm (about 3 times its diameter). The segments are placed side by side so we can work out how many there are by dividing the diameter of the wire into the length of the cylinder: 18/0.6=30.

So we now know that we need 30 segments of wire, where each segment is 49π cm long. The volume of the segment of wire is length times cross-sectional area, π(0.3)^2=0.09π sq cm, so the volume of a segment is 49π*0.09π cc=43.5250cc. There are 30 of these side by side so the total volume is 30*43.5250=1305.75cc. The length of wire is 30*49π=4618.14cm.

This is a fair approximation, because each segment will actually be slightly longer so as to join up with the next segment to form a continuous length, but because the cylinder's dimensions are very much greater than the wire's as a cylinder, the difference won't be significant. So 4618cm and 1306cc should be accurate enough for the length and volume of wire.

answered Feb 16 by Top Rated User (478,380 points)