self Maths Puzzle

A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?

Read Solution (Total 1)

Imagine and try to unfold the cylinder to form a rectangle:
Height = 108cm
Width = 24cm (circumference of the cylinder)
The string thus creates 6 diagonal lines whose measure can be found out by considering the 6 right triangles they can form:
Height of the cylinder dividing into 6 parts = 108/6 = 18cm
Now there are 6 triangles with Base = 24cm & height = 18cm
By using Pythagorean theorem: hypotenuse = sqrt(24^2 + 18^2)
Hypotenuse = 30cm
As there are 6 triangles so total length of the string = 6 * 30 = 180 cm
12 years agoHelpfull: Yes(4) No(0)

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