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If a piece of wire 30 cm long is bent into the form of an 
arc of a circle, subtending an angle of 60° at its centre, then radius of the circle is :
a)90 /π cm
b)45 /π cm
c)60 /π cm
d)30 /π cm
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If a piece of wire 30 cm long is bent into the form of anarc of a circ...
Given :
A piece of wire is bent in the form of an arc of a circle, of length: 30 cm
Angle subtended : 60 degree

Solution :
Here,
A wire of 30 cm subtends an angle of 60 degree or π/3 at the center.
Now, if we have another wire long enough to form an entire circle, that circle will subtend an angle of 360 degree or 2π at the center.
So in the second case , the length of arc will be ,
30 cm  =  π/3
x cm   =  2π
Therefore, x = 180 cm

This is now the circumference of the circle,
Therefore , 2πr = 180
or r = 90 / π
 r = 28.6 cm (approx)

Final answer :
Hence, the radius of the circle is 90 / π or 28.6 cm.
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Most Upvoted Answer
If a piece of wire 30 cm long is bent into the form of anarc of a circ...
Length of arc = 30 cm
So, 2 x 5 – 5p + 2 = 0
⇒ 10 + 2 – 5p = 0
⇒ 5p = 12
⇒ p = 2.4
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Community Answer
If a piece of wire 30 cm long is bent into the form of anarc of a circ...
To solve this problem, we can use the formula for the length of an arc of a circle. The formula is given by:

Length of arc = (θ/360) * 2πr

where θ is the angle subtended by the arc at the center of the circle, and r is the radius of the circle.

The problem states that the wire is bent into the form of an arc of a circle, subtending an angle of 60° at its center. The length of the wire is given as 30 cm.

Let's substitute these values into the formula and solve for r:

30 = (60/360) * 2πr

We simplify the equation:

30 = (1/6) * 2πr

Multiply both sides by 6:

180 = 2πr

Divide both sides by 2π:

90/π = r

Therefore, the radius of the circle is 90/π cm.

Explanation:

- We use the formula for the length of an arc of a circle: Length of arc = (θ/360) * 2πr
- Substitute the given values into the formula: 30 = (60/360) * 2πr
- Simplify the equation: 30 = (1/6) * 2πr
- Multiply both sides by 6: 180 = 2πr
- Divide both sides by 2π: 90/π = r
- Therefore, the radius of the circle is 90/π cm.

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If a piece of wire 30 cm long is bent into the form of anarc of a circle, subtending an angle of 60° at its centre, then radius of the circle is :a)90 /π cmb)45 /π cmc)60 /π cmd)30 /π cmCorrect answer is option 'A'. Can you explain this answer?
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