A cylinder

A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the top and bottom. (forming a spiral around the cylinder).
How long is the string in cm?

Correct result:

x =  180 cm

Solution:

$$\begin{gathered} h=108\text{ cm } \\ c=24\text{ cm } \\ c=2\pi \cdot r \\ r=c\mathrm{/}(2\pi )=24\mathrm{/}(2\cdot 3.1416)\doteq 3.8197\text{ cm } \\ x=\sqrt{h^2+(6\cdot c{)}^2}=\sqrt{108^2+(6\cdot 24{)}^2}=180\text{ cm} \end{gathered}$$

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Showing 2 comments:

Dr Math

Finding the length of the string is the same as finding the length of the hypotenuse of a triangle with a height of 48 cm and a base of a number of turns*circumference

2 years ago  Like

Math student

Can u put this in sixth grade math terms

2 years ago  Like

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