Question

A truck with 18 wheels has a tire radius of 21in. and a profile, or tire width, of 12in. If 20% of the tire is making contact with the ground what is the total surface area of the tires that is making contact with the ground at any one time?

Answer 1

`color(blue)(1814.4pi \ \ \ \"square inches")`

Explanation:

If we were to cut the tyre across the width and roll it out, it would form a rectangle, with length equal to its circumference and width equal to the tyre width.

Circumference of tyre:

`C=2pir`

`C=2pi(21)=42pi`

So the rectangle will have dimensions:

`42pixx12 \ \ \ \"inches"`

`Area"=42pixx12=504pi`

We are told that `20%` of this area is in contact with the road:

`20/100xx504pi=100.8pi`

There are 18 wheels so:

`18xx100.8pi=1814.4pi\ \ \"square inches"`