Find the exact circumference of a circle with a diameter of 5 inches.

##5pi## or 15.7 inches

Since the question gave you the diameter, the formula is

##color(blue)(Circumference) = color(red)(diameter)*pi##

If you look at the photo above, you can see that

##color(red)(diameter)## is the distance from one end of the circle to the other end that passes through the center of the circle. This is also 2 times the distance of the radius (2##color(green)r##)

##color(green)(radius)## is the distance from the center of the circle to any point on the edge of the circle

##color(blue)("circumference")## is basically the distance around the circle.

So why is the formula ##color(blue)C = color(red)dpi##?

It's been discovered that regardless of the circle size, the ratio of ##(color(blue)(C))/(color(red)d)## is always going to be 3.14, aka ##pi##. We write ##pi## so we don't have to memorize tons of decimal digits, although there are people who still do that for fun :)

Really, the ##color(blue)("circumference")## came from this formula ##(color(blue)(C))/(color(red)d)=pi##

so you can also write the formula as ##color(blue)C = color(red)dpi##

** If you're given the ##color(green)(radius)## of the question, just remember that diameter is two times the distance, and multiply ##color(green)r## by two first.

Okay, now let's look at the question. We are told that the ##color(red)(diameter)## is 5. Therefore,

##color(blue)C = color(red)5pi##

Sometimes the teachers will want you to multiply it out, sometimes they won't.

In higher level math, they'll want you to keep the ##pi## since it's more accurate than rounding out the answers, but check with your teacher just in case.