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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.

## Want to join the conversation?

• At to , couldn't he find the area and then multiply it by 3/4 and you get an answer? •  Sure, if what you needed was the area. But the exercise is asking for the arc length which is part of the circumference and not the area. Just remember that arc length, and circumference for that matter, is a measurement of length as the name implies while area is not.
• Is it the area or the circumference we're finding?
And rather than 2 pi r i'd use pi d. Is that okay? • does anyone have a word problem example for this? I believe it could help me comprehend this a little more. • 1st problem:
You need to bake a circular cake for a birthday party, the radius of the cake is 2dm (=20cm).
Looking from above, you want half the circle to be covered in ice sugar, the other half will be covered in chocolate powder.
Now you want to go an buy the ice sugar. At the shop, the ice sugar is sold in little bags for "1 dm2 cake coverage" (weird shop, I know, but it's the only one open :-) )
How many bags do you need to buy?

To answer, the easiest is to calculate the surface area of the whole cake, then divide it by 2 (because the rest will be covered in chocolate)
Surface area of the whole cake: Pi*(radius)squared = Pi*(2)squared = 4*Pi,
Half of the cake's surface area = (4*Pi)/2 = 2*Pi = approx. 6.28dm2,
So you'll need at least 7 bags to cover the part you want to cover.

For the second problem:
Now you decide you want to put the cake on a wooden circular stand. The stand's radius is 4 dm. You want to decorate all around the perimeter of the stand. You're thinking of using golden paper for 3/4 of the circumference, then you'll use red paper for the rest (1/4 of the circumference)
Now you want to purchase some golden paper. What length do you need to buy?

To calculate the length (= the arc length) you need to calculate the whole circumference first and then multiply it by 3/4 to find the length you really want:
Whole circumference = 2*Pi*radius = 8*Pi = approx. 25.13dm,
The length that you need: (8*Pi) * (3/4 ) = 6*Pi = approx. 18.85dm.

Hope that helps!
• still couldn't find the arc after 7 tries • 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!
• How do you find the quarter of a circles area • "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 • 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. :)  