Question 4 of 50intermediate🔧 ApplyNumerical2 marks

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use π = 22/7).

Correct Answer

12° 36′

Exercise: EXERCISE 3.1 | Q: 4 | (Page 7)
For More Understanding

Explanation

The problem requires finding the angle subtended by an arc at the center of a circle. The context provides the relationship between arc length (l), radius (r), and angle in radians (θ) in Example 3, where r = l/θ, which implies θ = l/r. After calculating the angle in radians, the conversion to degrees is done using the relation π radian = 180°, as described in section 3.2.4 and demonstrated in Example 2.

Solution Steps

  1. Step 1: Calculate the angle in radians using the formula θ = l/r. Given l = 22 cm and r = 100 cm, we have θ = 22/100 = 11/50 radians.

  2. Step 2: Use the conversion relation π radian = 180° to convert radians to degrees. θ = (11/50) × (180°/π).

  3. Step 3: Substitute the value of π = 22/7. θ = (11/50) × (180×7180 \times 7/22) = (1/50) × (180×7180 \times 7/2) = 1260/100 = 12.6°.

  4. Step 4: Convert the decimal degree into minutes. 0.6° = 0.6×600.6 \times 60′ = 36′. Thus, the angle is 12° 36′.

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