Question

In baseball, the pitcher's mound has a diameter of 18 feet. What is the circumference of the pitcher's mound?

Answer 1

`18pi~~ 56.549" feet"`

Explanation:

`"the circumference(C) of a circle is found using the formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(C=pid=2pir)color(white)(2/2)|)))`

`"where d is the diameter and r is the radius"`

`"here "d=18`

`rArrC=pid=18pilarrcolor(blue)" exact value"`

`"or "C~~56.549" feet to 3 dec. places"`

Answer 2

So that you understand what is happening

Explanation:

There is a unit of measurement called a Radian. This is a segment of a circle where the length of the curve is the same as the length of the radius.

So if we know how many of these will fit on to a circle and we also know the value of `r` we can work out the distance round the outside of the circle (Circumference).

This is where that special number of `pi` comes in. There are `2pi` radians in a circle.

So the circumference length is `2pi` lots of `r`

The diameter in this question is 18 feet. So the radius is half of this giving `r=9` feet

Thus the circumference is:

`2pixx9 = 18pi` as an exact value and 56.55 to 2 decimal places as an approximate value.
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By the way `2pir` is the same as `pixx(2xxr) = piD` where `D` is the diameter of the circle.