**Solution:**
To make visualization easy, it is convenient to conceptually open out the bark of the tree trunk and flatten it. The cylindrical surface will then be a rectangle (as illustrated in the figure alongside for 4 twists of the creeper).

It may be noted that:

Width of the rectangle = Circumference of the cylinder = 40 inches.

Height of the rectangle = Vertical distance on the cylinder = 75 inches (in one twist).

Using the Pythagorean Theorem for a right-angled triangle,

Length of the hypotenuse = (40

^{2} + 75

^{2})

^{1/2} = 85 inches.

Now, the number of twists the creeper makes around the tree trunk is 6 (= 450 / 75).

If the length of the creeper (as given by the hypotenuse) is 85 inches in one twist, then the total length of the creeper in 6 twists is 510 inches.

**Food for thought:**
Is the total length of the creeper in the above calculation the actual length or the minimum length?