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The shaded area below has a area of 4pi. Find the perimeter of the sector.

 Jun 13, 2020
 #1
avatar+8341 
0

We first find the radius,

 

Let r be the radius.

 

\(\dfrac{40^\circ}{360^\circ} \cdot \pi r^2 = 4\pi\\ r = 6\)

 

Then we can use the formula \(P = \dfrac{\theta}{360^\circ} \cdot \left(2\pi r\right) + 2r\) to calculate the perimeter of the sector.

I believe you can finish it on your own.

 Jun 13, 2020
 #2
avatar+338 
-1

Answer:

10.19

Step-by-step explanation:

40°=360°/9=2π/9

area of circle= πr²

Area of sector= πr²/9

πr²/9=4π ⇒ r²=4*9 ⇒ r²=36 ⇒ r=6

P circle= 2πr

P sector= 2r+2πr/9= 6+2*3.14*6/9 = 6+4.19= 10.19

 Jun 13, 2020

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