Question

how many full revolutions does a car tire with a diameter of 25 in make when the car travels one mile?

Answer 1

A car tire makes 807complete revolutions when it travels 1 mile.

Explanation:

Diameter of tire = d = 25 inches

Radius of the tire = r =
`(d)/(2)=(25 inche)/(2)=12.5 inches`

Circumference of circle = 2πr

Circumference of tire =
`2* 3.14* 12.5 inches = 78.5 inches`

1 mile = 63,360 inches

In single revolution tire, tire covers 78.5 inches.

let number of revolution in 1 mile x.

`63,360 inch=x* 78.5 inch`

`x=(63,360 inch)/(78.5 inch)=807.13\approx 807`

A car tire makes 807complete revolutions when it travels 1 mile.

Answer 2

`807\ rev`

Explanation:

we know that

The length of the circumference of a circle represent one revolution

so

The circumference of a circle is equal to

`C=\pi D`

we have

`D=25\ in`

substitute

`C=\pi (25)=25\pi\ in`

Remember that

`1\ mi=63,360\ in`

so

by proportion

Find how many full revolutions does a car tire make when the car travels one mile

`(1)/(25\pi)(rev)/(in)=(x)/(63,360)(rev)/(in)\\ \\x=63,360/(25\pi)\\ \\x=806.7\ rev`

Round to the nearest whole number

`806.7\ rev=807\ rev`