NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles - Exercise 11.3Question 16
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles - Exercise 11.3
Question. 16
A piece of wire 20 cm long is bent into an arc of a circle subtending an angle of \(60^\circ\) at the centre. Find the radius of the circle.
Answer:
\(\dfrac{60}{\pi}\;\text{cm}\) (≈ 19.10 cm)
Detailed Answer with Explanation:
Step 1: Recall the formula for arc length of a circle:
\( s = r \theta \)
where,
- \(s\) = arc length (in cm)
- \(r\) = radius of circle (in cm)
- \(\theta\) = angle at the centre (in radians)
Step 2: Write down the given values:
- Arc length, \(s = 20\,\text{cm}\)
- Angle, \(\theta = 60^\circ\)
Step 3: Convert the angle into radians, because the formula works in radians.
\(60^\circ = \dfrac{60 \times \pi}{180} = \dfrac{\pi}{3}\,\text{rad}\)
Step 4: Substitute the values into the formula:
\( s = r \theta \)
\( 20 = r \times \dfrac{\pi}{3} \)
Step 5: Solve for \(r\):
\( r = \dfrac{20}{\pi/3} = \dfrac{20 \times 3}{\pi} = \dfrac{60}{\pi}\,\text{cm} \)
Step 6: Approximate the value using \(\pi \approx 3.14\):
\( r \approx \dfrac{60}{3.14} = 19.10\,\text{cm} \)
Final Answer: The radius of the circle is \(\dfrac{60}{\pi}\,\text{cm}\) or about 19.10 cm.