Question 20 of 42intermediate🔧 ApplyNumerical3 marks

Find the area of a quadrant of a circle whose circumference is 44 cm.

Correct Answer

38.5 cm²

Exercise: Exercise Set 6.3 | Q: 2 | (Page 31)
For More Understanding

Explanation

The question requires finding the area of a quadrant given the circumference. First, the radius is derived from the circumference formula C = 2πr. Using π ≈\approx 22/7 as specified in the context, the radius is calculated as 7 cm. Next, the area of the quadrant is found using the formula (1/4)πr², as a quadrant represents a quarter of a circle's area. Substituting the values gives 38.5 cm².

Solution Steps

  1. Step 1: Use the circumference formula to find the radius: 2 × (22/7) × r = 44, which gives r = 7 cm.

  2. Step 2: Calculate the area of the quadrant using the formula (1/4)πr²: (1/4) × (22/7) × 7² = 38.5 cm².

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