Question 46.
Suppose that eight turns of a wire are wrapped around a pipe with length of 20 cm and a circumference of 6 cm. What is the length of the wire?
Answer 46.
If you cut the cylinder along a line parallel to its axis and open up it will be a rectangle of length 20 cm and width 6 cm. As there are 8 turns, pitch of turns will be 2.5 cm. Now from one corner of the rectangle, draw a line on the opposite side of rectangle 2.5 cm from the opposite corner. It becomes the hypotenuse of a right triangle of sides 2.5 cm and 6 cm. 8 such lines can be drawn on the rectangular sheet which form the eight turns of the wire.
Hence, length of wire needed
= 8 * sqrt [ (2.5)^2 + (6.0)^2 ] cm
= 52 cm.
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