Question

A thin copper wire is wound, uniformly and spirally, in a single layer, from the bottom to the top, around a cylindrical iron rod. the circumference of the iron rod is 2 cm. and its height is 56 cm. if the number of turns in the spirally wound copper wire is exactly 45, what is the length of the copper wire used?

Answer 1

Since this wire is spiral, we will assume we have a right angled triangle.

We will then use pythagoras theorem to get the length of the wire.

Now :

We have a right angled triangle whose :

Base = Circumference of the circle × Number of turns

Height = Height of the cylinder.

Hypotenuse = The length of the wire

Therefore :

Base = 45 × 2 = 90 cm

Height = 56 cm

By Pythagoras theorem :

Hypotenuse² = 56² + 90²

= 11236

Hypotenuse = √11236 = 106

The length of the wire is thus 106 cm