Question

an arc of a circle is of length 5 pi cm and sector it bounds has an area of 20 pi cm2. find the radius of the circle.

Answer 1

Let the radius of the circle = r cm 

Given, length of an arc of the circle = 5 

π 

Cm and area of sector=  

20 π cm square 

We know that, length of an arc of the circle  

= θ(2π r)/360 Degree 

Which is equal to 5 π 

  θr=900 

     π = 900/r ----- (I) 

Area of sector = π r square  θ/360 Degrees 

= 20 π 

R square   θ 

= 7200 -----(ii) 

Substitute value of  

 θ 

Hence the radius of the circle is 8cm

Answer 2

Answer:

Step-by-step explanation:

Let the radius of the circle be r cm and the arc AB of length 5πcm subtends angle theta at the centre O of the circle. Then,

 Arc AB =5π cm and Area of sector OAB = 20π cm^2

theta/ 360 ×2πr = 5π

theta/360 × πr^2= 20π

theta/360×πr^2/theta/360×2πr = 20π/5π

= r/2 =4

= r =8