Question

Question on radius, arc length, area of sector (will attach picture)

Answer 1

Here is the question! Thanks! :D

Answer 2

Start with the area and circumference formulas for circles. You'll need both since there are two unknowns to solve for.

Answer 3

The thing that connects the two equations is that for both, the part (fraction) of the circle is the same. You can use that fact to set up a proportion.

Answer 4

\[\frac{4\pi/3}{A}=\frac{2\pi/3}{C} : A=\pi r^2, C=2\pi r.\]

Answer 5

Once you have radius from the above. Use the arc length formula to solve for Θ.

Answer 6

Oh, thanks! I'll try it out :D

Answer 7

y.w. Please post your solutions so I can check my own work.

Answer 8

would the radius of the circle be 4?

Answer 9

That's what I got. :-)

Answer 10

is it possible, since the area of a sector is \[\frac{ \theta }{ 2 }r ^{2}\ = \frac{ 4\pi }{ 3 }\]
and the area of the arc is \[s = \theta r \] we can rewrite it as

\[r = \frac{ \frac{ 2\pi }{ 3 } }{ \theta }\]

then we can rewrite the whole equation as

\[\frac{ \theta }{ 2 }\left( \frac{ \frac{ 2\pi }{ 3 } }{ \theta } \right) = \frac{ 4\pi }{ 3 }\]

Answer 11

@brygiger , no, that is an identity and the variable cancels out, making it impossible to solve.

Answer 12

sorry, i what about squarig the 2πr/theta, i forgot

Answer 13

*2π/3/theta

Answer 14

Though I think you meant to square the (2π/3)/Θ in that last equation. If so it would look like this:
\[\frac{θ}{2} \cdot (\frac{2π}{3θ})^2=4π3 \rightarrow \frac{θ}{2} \cdot \frac{4π^2}{9θ^2} = \frac{2π^2}{9θ}\]

Answer 15

Yes, that will work if you want to solve for Θ first.

Answer 16

ok cool thanks! yours is much more simpler though haha

Answer 17

2/3π = 2πr (θ/360), so i merely have to input the values right? That would give me approximately 969 degrees... is that correct?

Answer 18

er.. no. The arc length formula is s=rΘ, so Θ=s/r.

Answer 19

If arc length is 2π/3 then Θ=(2π/3)/4.

Answer 20

is the answer 30 degrees?

Answer 21

oh so sorry =)) so the answer is 30 degrees then! Thanks! :D