[Instinct01]

Hi,

Would someone please explain to me the difference between the perimeter of a circle and the circumference of a circle? After having Googled it, I read that perimeter is interchangeable with circumference on numerous sites, as well as some videos.

Then, why, during some exercise questions have I found the circumference to not be equal to the perimeter of a circle? For example:

Calculate the perimeter of a semi-circle with radius of 7.5cm.

If you were to work out the circumference:
15*3.14 = 47.12
So, 47.12/2 = 23.57

But I noticed the answer was always the circumference plus the diameter to obtain the value of the perimeter. So why are these words used interchangeable when they have different values?

Thanks for any explanations.

[7589200]

they're the same thing

[Instinct01]

(Original post by Vazzyb)
they're the same thing

Thanks. But could you explain why the circumference of a semi-circle with radius of 7.5cm is 23.57cm, but the perimeter of a semi-circle with radius of 7.5cm is 38.6cm?

[Dark Lord of Mordor]

The perimeter is the general term for all shapes (total length of sides), whereas the circumference is purely for circles

[You Failed]

(Original post by Instinct01)
Thanks. But could you explain why the circumference of a semi-circle with radius of 7.5cm is 23.57cm, but the perimeter of a semi-circle with radius of 7.5cm is 38.6cm?

Because a circle =/= a semi circle....

[danny111]

I think the "circumference" of a semi-circle they mean just the bendy part, not the straight line. Although I am not sure if you are allowed to call that circumference. Perimeter includes the straight line.

For a whole circle they are the same. Thats the only reason I can think of.

[Instinct01]

(Original post by You Failed)
Because a circle =/= a semi circle....

Thank you! The first answer which has actually answered what I was looking for. But why isn't the formula for a circumference of circle the same for that of a semi-circle (apart from dividing by 2). I mean, the area follows that rule, right?

[chill543]

(Original post by You Failed)
Because a circle =/= a semi circle....

yeah.... i didnt realise that it was a semi circle, only really read the first bit...was well confused....

[Instinct01]

(Original post by danny111)
I think the "circumference" of a semi-circle they mean just the bendy part, not the straight line. Although I am not sure if you are allowed to call that circumference. Perimeter includes the straight line.

For a whole circle they are the same. Thats the only reason I can think of.

Ah, I see. Thank you very much, makes a lot of sense now

[thefifthfoo]

(Original post by Instinct01)
Thank you! The first answer which has actually answered what I was looking for. But why isn't the formula for a circumference of circle the same for that of a semi-circle (apart from dividing by 2). I mean, the area follows that rule, right?

Well yes, but the straight line part of the perimeter of a semicircle is not part of the circumference/perimeter of a circle, it s just the diameter (and entirely contained inside the circle. The formula is the same (apart from dividing by 2) if you only want to know the length of the curved bit (the bit that forms half of the whole circles circumference). Then you have to add on the straight bit. Draw a picture of a circle and semicircle next to each other and this should become very obvious

[aznkid66]

Given that the definition of circumference is the distance around a closed curve, the circumference should always equal the perimeter, which is the distance around a closed figure. Thus, from this definition, the circumference of a semi-circle is also (pi+2)r.

If the source you are learning from says that the circumference of a semi-circle is the arc length, then all we can say is that your source does not define circumference as equivalent to perimeter, so we cannot provide a "mathematical" explanation.

[TLHroolz]

In a semi-circle the perimeter would include the straight at the bottom whereas the circumference wouldn't. They are the same thing in a full circle


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