Help me find the area and arc length of a circle?

Question

I am provided that the radius of the circle is 2 and that the angle is 210 degrees.


I know that the following formulas must be used
s=r (delta)
A=1/2 r^2 (delta)

the answer i get for area is about 7.33
and for arc length i get about 7.33 too.

Can someone please help me verify to see if this is correct.

I am certain that I must change the angle to radians for this to work.

Answer 1

r = 2
angle = 210

arc length = 210 * phi/180 * 2
= 7.33

area = 210/360 * phi * 2^2
= 7.33

yup, it's the same answers..

Answer 2

The arc length of a circle is given by this formula.
s = 2*pi*r. ( s is the arc length and r is the radius)
The area is for a circle is given by this formula.
A = pi*r^2 (A for Area)

In your problem you don't need the area or arc length for the whole circle just a sector of it so all you have to do is to see how 210 degrees relate to the 360 degree ( the whole circle).

210/360 = 21/36 = 7/12

So your sector Area (A1) and Arc length (S1) is 7/12 of the whole circle Area and Arc length.

S1 = 7 * S / 12 = 7 * 2 * pi * r / 12 = 7 * pi * r / 6
A1 = 7* A / 12 = 7 * pi *r ^ 2 / 12

in your case radius is 2 so

S1 = 7 * pi * 2 / 6 = 7 * pi / 3
A1 = 7 * pi * 4 / 12 = 7 * pi / 3

In this case A1 = S1

a approximation for pi is 22 / 7 ( Not very good one )

gives S1 and A1 are approximated to

7 * 22 / (7 * 3) = 22 / 3

which is the same as your answer.

However a better approximation can change the last digits

like using 3.141 592 654 as pi.

Answer 3

Arc length is in simple terms the stages of the mandatory perspective. yet first, you would be able to desire to be certain what % of the circle one hundred stages is. you realize that there are 360 stages in a circle, hence one hundred stages is one hundred/360 % of the completed circle. Then discover circumference. it fairly is 2pier , r is 4 subsequently, which equals 8pie for circumference. Now multiply the full circumference by way of (one hundred/360) What you're doing is multiplying what the ratio is from the section sector of the completed circle, so which you will desire to get an answer that expresses the arc length of that section for one hundred stages in that circle. you will desire to get 20pie / 9 as your answer, or 2.22222pie or, 6.ninety 8 (rounded)

Answer 4

the area of the whole circle would be
pi r^2
but since you want 210 deg out of 360 you have to multiply by (210/360)
A= 3.14*(2^2)*(210/360)= 7.33
the arc length is just the radius time the angle in radians
angle = (210/360)*2*pi= 3.66 radians
arc length=2*3.66=7.33

you were right!

Answer 5

Yes, you do need to change the angle to radians.
Multiple by pi/180 = 3.67 (this value will be x)

arc length l=rx
= 3.665*2
=7.33 units

area = 1/2 r^2 x
= .5*2^2*3.665
= 7.33 units^2

Your answers look correct, make sure you include the correct units.

Answer 6

Area of circle = πr² = 4π units²
Area of sector = (210/360) x 4π = 7.33 units²

Circumference = 2 π r = 4π units
Arc length = (210/360) x 4π units = 7 .33 units

It would appear that we are in agreement!

Answer 7

S = 2 * pi * r
A = pi * r^2

for 210 degrees

S = 2 * pi * r * 210 / 360
A = pi * r^2 * 210 / 360