If the tie on a bike has a radius of 12 inches, how far will the bike travel in 100 rotations?

1 Answer
Mar 15, 2018

See a solution process below:

Explanation:

First, we need to determine the circumference of the bike's tire. The formula for the circumference of a circle is:

#C = 2pir#

Substituting the radius of #12"in"# for #r# gives a circumference of:

#C = 2pi12"in"#

#C = 2 * 12pi"in"#

#C = 24pi"in"#

So, ever time the tire rotates it travels #24pi# inches.

To find how far it travels if it rotates 100 times we multiply the circumference by #100# giving:

#100 xx 24pi"in" => 2400pi"in"#

We can approximate #pi# as #3.14# giving:

#2400 * 3.14"in" => 7536"in"#

The bike would travel 7536 inches

Or

#7536"in" xx (1"ft")/(12"in") => 7536color(red)(cancel(color(black)("in"))) xx (1"ft")/(12color(red)(cancel(color(black)("in")))) => 628"ft"#

Or

#628"ft" xx (1"mi")/(5280"ft") => 628color(red)(cancel(color(black)("ft"))) xx (1"mi")/(5280color(red)(cancel(color(black)("ft")))) => 0.12"mi"# rounded to the nearest hundredth of a mile.