From an iron ring of radius 18 centimetres, a piece of central angle 30° is cut off . This is then bent into a small circle. What is the radius of this circle?
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Given : From an iron ring of radius 18 centimetres, a piece of central angle 30° is cut off . This is then bent into a small circle.
To Find : What is the radius of this circle?
Solution :
iron ring of radius 18 centimetres,
Circumference of Circle = 2π(Radius)
Circumference of original ring = 2π (18) = 36π cm
a piece of central angle 30° is cut off
Hence arc length cut = (30/360) 36π = 3π cm
Remaining length of ring = 36π - 33π = 33π cm
Circumference of new circle = 33π cm
2π R = 33π
=> R = 33/2
=> R = 16.5 cm
radius of this new circle = 16.5 cm
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Given :- From an iron ring of radius 18 cm, a piece of central angle 30° is cut off . This is then bent into a small circle.
To find :-
- What is the radius of this circle ?
Solution :-
we know that,
- circumference of circle = 2 * Π * radius .
- Length of arc = (Angle at centre/360°) * 2 * Π * radius .
so,
→ circumference of iron ring = 2 * Π * 18 = 36Π cm
now, putting value of angle and radius we get ,
→ Length of arc = (30/360) * 2 * Π * 18 = (1/12) * 36Π = 3Π cm.
then,
→ Remaining piece of iron ring = circumference of iron ring - Length of arc = 36Π - 3Π = 33Π cm.
now given that this remaining piece of cut is bent to form a small circle .
then,
→ circumference of small circle = remaining piece of iron ring
→ 2 * Π * radius = 33Π
→ 2 * radius = 33
→ radius = 33/2 = 16.5 cm (Ans.)
Hence , the radius of small circle will be 16.5 cm .
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