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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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• still couldn't find the arc after 7 tries
• "Try Try but don't cry"
Always remember this quote and go forward!
:) :>
(1 vote)
• i still dont know how to do this
• 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
A is the central angle(angle formed by the 2
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
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!
• At , why do you multiply 3/4?
• 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. :)
• "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
• 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.
• 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).
• 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
• If you want 1 quarter and you have 3 quarters you can just divide by 3 to get 1 quarter
• queen elizabeth died yesterday
• When I get the wrong answer and I click Get Help it says a completely different problem than the video shows.