Question 5 of 50intermediate🔧 ApplyNumerical3 marks

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Correct Answer

The length of the minor arc is 440/21 cm (or approximately 20.95 cm).

Exercise: EXERCISE 3.1 | Q: 5 | (Page 7)
For More Understanding

Explanation

This question requires understanding the relationship between chord length, radius, and arc length. The key insight is recognizing that when chord length equals radius, the triangle formed is equilateral, making the central angle 60°. Then applying the arc length formula l = rθ from the textbook.

Solution Steps

  1. Step 1: Given diameter = 40 cm, therefore radius r = 20 cm. Chord length = 20 cm.

  2. Step 2: Let chord be AB and O be the centre. In triangle AOB, OA = OB = 20 cm (radii) and AB = 20 cm (given).

  3. Step 3: Since OA = OB = AB = 20 cm, triangle AOB is an equilateral triangle. Therefore, angle AOB = 60°.

  4. Step 4: Converting angle to radians: θ = 60° = 60 × π/180 = π/3 radian.

  5. Step 5: Using formula l = rθ from the context, l = 20 × π/3 = 20π/3 cm.

  6. Step 6: Using π = 22/7, l = 20×2220 \times 22/(7×37 \times 3) = 440/21 cm ≈\approx 20.95 cm.

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