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 cylinder's top and bottom. (forming a spiral around the cylinder).
How long is the string in cm?

Result

x =  180 cm

Solution:

h=108 cm c=24 cm  c=2π⋅ r r=c/(2π)=24/(2⋅ 3.1416)≐3.8197 cm  x=h2+(6⋅ c)2=1082+(6⋅ 24)2=180 cmh=108 \ \text{cm} \ \\ c=24 \ \text{cm} \ \\ \ \\ c=2 \pi \cdot \ r \ \\ r=c/ (2 \pi)=24/ (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}

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Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

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

#
Math student
Can u put this in sixth grade math terms

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