SOLUTION: A wheel 4 ft. in diameter makes x revolutions. Find x, given that the distance traveled by a point on the circumference of the wheel is 23169 ft. Round your answer to the nearest w

Question 110618: A wheel 4 ft. in diameter makes x revolutions. Find x, given that the distance traveled by a point on the circumference of the wheel is 23169 ft. Round your answer to the nearest whole number.
The answer is 1844 revolutions but I can't figure out how to get there.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The circumference of a circle (or wheel) is the distance around the outside. It is given
by the formula:
.
C = pi*D
.
where D is the diameter of the wheel and pi is a special number that is never ending but
is 3.14159265 ...... and for most purposes can be shortened to 3.1416
.
This means that for our equation we can use:
.
C = 3.1416*D
.
and we are told that the diameter of the wheel is 4 feet. That means that the distance
around the outer edge of the wheel is:
.
C = 3.1416*4 feet
.
and if you do the multiplication you get:
.
C = 12.5664 feet.
.
So if you put a mark on the outer rim of the wheel, and you rotate the wheel once,
that spot will travel a distance of 12.5664 feet.
.
The problem tells you that a spot on the wheel is known to have traveled 23169 ft and
asks you to find the number of complete turns or revolutions that the wheel had to make to get
the spot to move that far. Since each turn gives 12.5664 ft you can just divide 23169 by 12.5664
to find the number of turns.
.
Calculator time:
.

.
So if the wheel revolves 1843.726 times (rounded to 1844 times) the total distance
traveled by a spot on the wheel will be about 23169 feet.
.
Hope this helps you to understand the problem.

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