Question 1 of 7intermediate🔧 ApplyNumerical3 marks

Find the area of a quadrant of a circle whose circumference is 22 cm.

Correct Answer

The area of the quadrant is 9.625 cm².

Exercise: EXERCISE 11.1 | Q: 2 | (Page Page 5)
For More Understanding

Explanation

This is a direct application of the sector area formula from the textbook. A quadrant is a sector with angle 90°. The key step is first finding the radius from the given circumference using the formula 2πr, then applying the sector area formula (θ/360) × πr².

Solution Steps

  1. Step 1: Find the radius from the circumference. Given circumference = 22 cm. We know that circumference = 2πr. So, 2πr = 22, which gives r = 22/(2π) = 22/(2×222 \times 22/7) = 22×722 \times 7/44 = 7/2 = 3.5 cm.

  2. Step 2: A quadrant is one-fourth of a circle, so the angle of the sector is θ = 90°.

  3. Step 3: Apply the formula for area of a sector: Area = (θ/360) × πr². Substituting the values: Area = (90/360) × (22/7) × (3.5)² = (1/4) × (22/7) × 12.25 = (1/4) × 38.5 = 9.625 cm².

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