Diameter

[Guest]

A hard rubber tire has a defect in the tread which causes a cut mark in the tire track every 36 inches.

Calculate diameter of the tire.

Thanks for your assistance.

[Guest]

Do you want assistance or do you want the question answered for you....????

The circumference of a circle is calculated by multiplying the diameter by Pi.

Pi is the ratio of the circumference to the diameter of a circle....

It s generally taken as a circle having a diameter of 7 units will have a circumference of 22 units.

This means most people take Pi as 22 divided by 7.......22/7....

In decimal form this works out as 3.142.

Every time the wheel rolls a complete circle the "cut" mark will have reappeared on the track so distance between the "cut" marks is the circumference of the circle......

If you are being asked by someone to do questions like these....you should be able to work it out for your self from the information I have given you......

If not then post a question stating what part you do not understand.....and we can help you....

[Guest]

I was not sure how to obtain the solution to the problem. I am just expressing my appreciation for the help. Anytime someone assists me, I thank them.

[Guest]

Ok, are you able to solve the problem now.....???

From my first post I stated that (circumference) = (Diameter) x ( Pi)

Or... written the other way round......(Diameter) x (Pi) = (Circumference)

If I divide bothe sides of the equation by (Pi), the (Pi)s on the left of the equation will cancel and the equation becomes...

(Diameter) = (Circumference) divided by (Pi)

So........(Diameter) = (Circumference) / (Pi)

We know the circumference of the wheel is 36 inches, that is how far the wheel rolls without slipping in one revolution.

So diameter of the wheel is...... (Diameter) = ( 36 ) / ( Pi)

......... Then (Diameter) = ( 36 divided by 3.142 )...and as a sum.... = ( 36 /3.142 ) = 11.46 inches

Or taking (Pi) as 22/7...... gives (Diameter) = ( 36 ) divided by ( 22/7 )
This is same as (36 x 7) / 22......to divide by a fraction, turn it upside down and multiply.

This gives diameter equal to.... 11.45 inches

So there is a slight difference depending on what you take for the value of ( Pi )

My calculator works out 22/7 as 3.1428 which is 3.143 to 3 decimal places.....

But I have always used 3.142 as that was the figure quoted in most of the textbooks I have used....
Some textbooks take ( Pi ) as 3.14....for simplicity.........

Mathematicians have argued over this for hundreds of years....................

..........Simple......

[Guest]

"distance between the "cut" marks is the circumference of the circle......"

It did not occur to me that is the circumference until after your explanation. I understand it now.

Thanks again.