Question

A certain machine is to contain two wheels, one of radius 2 inches and one of radius 8 inches. The manufacturer of this machine needs to produce a belt that will fit snugly around the two wheels, as shown in the diagram below. How long should the belt be?

Answer 1

See Below

Explanation:

The length of the belt is the length around 2 inch radius wheel PLUS length around 8 inch radius wheel.

The length around a circular region is its circumference. The formula is:

`C=2 \pi r`

Where

C is circumference

r is the radius

We sum up both, given first one radius is 2 and second one radius is 8, so we have:

`2\pi r + 2 \pi r \\=2 \pi (2) + 2 \pi (8)\\=4\pi + 16 \pi\\= 20 \pi\\=62.83`

The length of the belt should be around 62.83 inches