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Partial circle area and arc length

Sal finds the area of a semicircle and the arc length of a partial circle.

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  • aqualine ultimate style avatar for user Baldwin Louis Tyson
    still couldn't find the arc after 7 tries
    (10 votes)
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  • blobby green style avatar for user 25jagoins
    i still dont know how to do this
    (7 votes)
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    • starky seed style avatar for user Dishita
      Hey there!
      (Don't get scared! I know the answer is quite long, but very very simple)
      There's a generalized formula for calculating the arc---very simple when you realize the steps, I have derived it in the form of proportion:

      let x be the arc we are searching for
      C be the circumference
      C=2*pi*radius
      A is the central angle(angle formed by the 2
      radii)
      x:A::C:360 === 'arc' = C when central angle is 360 deg (complete circle), what would be arc if angle = A
      x=(C*A)/360
      That's it!

      if you're getting confused by the terms, let me help you out here,
      Circumference = perimeter of the circle
      arc = part of the circumference lying between 2
      radii(plural form of radius).
      central angle= angle formed by two radii...where? at the centre
      a question may arise here asking which central angle corresponds to which arc
      the larger the angle=larger the arc, you can then correlate.

      in one of the questions he mentioned above, the area(Pi*r^2) is given,
      to find the circumference we need to know the value of r(the only variable) then we can calculate the arc.

      Hope you understood and I hope I cleared your doubt but @25jagoins, it would be great if you state what you didn't understand and be a bit less vague while asking questions, it would help people help you.
      Keep up your consistency and don't give up!
      Onward!
      (4 votes)
  • hopper jumping style avatar for user Komal
    At , why do you multiply 3/4?
    (2 votes)
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    • piceratops ultimate style avatar for user fr33d0g
      Because the formula 2 π r is the formula for the circumference of the WHOLE circle. But they only want the arc length of 3/4 of the circle. So the answer of 8π was the answer for the whole circle so you have to multiply it by 3/4 which gives you 6π, The answer to the arc length that they asked for. :)
      (12 votes)
  • duskpin ultimate style avatar for user MemeVee
    "So pause this video and see if you can figure it out." Sal, I'm here to figure out HOW to solve these, not just guess and hope I'm right
    (5 votes)
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  • hopper happy style avatar for user Evelyn.271187@nv.ccsd.net
    Is finding the arc length of a partial circle the same procedure as finding the circumference of that same partial circle? If so, the arc length and the circumference of the same circle would be the same, right? I know how to find the arc length and circumference of a circle, but my results always seems to come out the same.
    (3 votes)
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    • duskpin ultimate style avatar for user Catherine Chen
      Yes, technically, the arc length of a partial circle would be the same as the circumference of that same partial circle. However, if you're trying to find the arc length of a partial circle, it's not the same as the circumference of the same circle wholly. You need to find out the circumference of the whole circle first before you can find the arc length (or the circumference of the partial circle).
      (4 votes)
  • aqualine tree style avatar for user Enzo gabriel
    Ummm so this shows 3/4 of a circle but how will you find 1/4 of one the problem I'm on is 1/4 and this is the only video it leads me to. Someone help me plz
    (3 votes)
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  • duskpin sapling style avatar for user Cameron
    queen elizabeth died yesterday
    (4 votes)
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  • winston default style avatar for user gabriel.stepp1
    When I get the wrong answer and I click Get Help it says a completely different problem than the video shows.
    (4 votes)
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  • aqualine ultimate style avatar for user whou
    How do you find the quarter of a circles area
    (0 votes)
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  • primosaur seedling style avatar for user Kaylee Blair
    I still don't get how you got 2 for the final answer after watching this video 16 times on the first question I just don't get how you can put numbers in a place and get them in just the right spot and get a final answer that is right and not an answer that is a just a little off or more than a little off? You know what I am saying?
    (3 votes)
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Video transcript

- [Instructor] Find the area of the semicircle. So pause this video and see if you can figure it out. So let's see. We know that the area of a circle is equal to pi times our radius squared. So, if we think about the entire circle, what is the area going to be? Well, they tell us what our radius is. Our radius is equal to two, so the area, if we're talking about the whole circle, it would be equal to pi times two squared. Pi times two squared. Two squared is of course two times two, which is equal to four, so our area is going to be equal to four times pi. Now, I wouldn't put four pi here, because that would be the entire circle. They want the area of just the semicircle, of just this region right over here. Well, the semicircle is half of the circle, so if I want the area of the semicircle, this is gonna be half this. So instead of four pi, it is going to be two pi square units. That's the area of the semicircle. Let's do another example. So here, instead of area, we're asked to find the arc length of the partial circle, and that's we have here in this bluish color right over here, find this arc length. And you can see this is going three fourths of the way around the circle, so this arc length is going to be three fourths of the circumference. So what is the circumference? Well, we know the circumference is equal to two pi times the radius. They tell us what the radius is. It's equal to four, so our circumference is equal to two pi times four. Let's see, we can just change the order in which we multiply so it's two times four times pi. This is going to be equal to eight pi. This is going to be equal to eight pi. Now, that is the circumference of the entire circle. If we care about this arc length, it's going to be three fourths times the circumference of the entire circle. So three over four times eight pi. What is that going to be? Well, what's three fourths times eight? Well, three times eight is 24 divided by four is six. So this is going to be equal to six pi. Another way to think about it, one fourth of eight is two, so three fourths is going to be six. Or another way to think about it is, one fourth of eight pi is two pi, and so three of those is going to be equal to six pi. So the arc length of the partial circle is six pi, and once again we knew that because it was three fourths of the way around. The way that I knew it was three fourths is that this is a 90 degree angle. This is 90 degrees, which is one fourth of the way around a circle, so the arc length that we care about is the three fourths of our circumference.