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.
Answers
Answered by
206
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
Answered by
165
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
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