Question

The cylinder below has a radius 3 inches and a height of 8 inches. If two points are located on the surface of the cylinder, what is the maximum straight line distance they could be a part?

Answer 1

Consider the two situations below:

1) Two points are located on opposite sides of a diameter; as in the next diagram

The distance between the two points is equal to the diameter of the circle; in other words, 2 times the radius. Thus, the distance between the two orange points above is 6in.

2) Consider two points on opposite faces of the cylinder

The distance between the two points is equal to 8in, in this situation.

Mixing both diagrams so as to obtain the maximum distance between two points on the cylinder,

Thus, the maximum distance is given by the Pythagorean theorem, as shown below

`d_(max)=√(6^2+8^2)=10`

Hence, the answer is 10in