Question

an arc of a circle is of length 5 pi cm and sector it bounds has an area of 20 pi cm 2 . find the radius of the circle.

Answer 1

Solution:-

Let the radius of the circle be 'r' cm.
Given : Length of an arc of the circle = 5π cm and area of the sector = 20π cm²
We know that, length of an arc of the circle = θ(2πr)/360°
Therefore,
θ(2πr)/360° = 5π
⇒ θr = 180*5
⇒ θr = 900
⇒ θ = 900/r .........(1)
And,
Area of the sector = πr²θ/360°
Therefore,
πr²θ/360° = 20π
⇒ r²θ = 360*20
⇒ r²θ = 7200 ...........(2)
Substitute value of θ from equation (1) in the equation (2), we get
⇒ r²(900/r) = 7200
⇒ r = 7200/900
⇒ r = 8 cm
Answer.

Answer 2

Answer:

Let the radius of the circle = r cm 

Given, length of an arc of the circle = 5 

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 

 θ=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

Step-by-step explanation: By fadhil faisal

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