Question 23 of 42intermediate🔧 ApplyNumerical3 marks

A chord of a circle of radius 10 cm subtends 90° at the centre. Find the area of the corresponding: (i) minor sector (that subtends 90° at the centre), and (ii) major sector (that subtends 270° at the centre). (Use π \approx 3.14.)

(i)
Answer

78.5 cm²

(ii)
Answer

235.5 cm²

Explanation

The question requires calculating the area of the minor and major sectors. The textbook context provides the formula for the area of a sector: πr² × (θ°/360°). For the minor sector, the angle is 90°, which makes it a quarter of the circle's area. For the major sector, the angle is 270° (360° - 90°), making it three-quarters of the circle's area. Using the given radius of 10 cm and π \approx 3.14, we can directly substitute these values into the formula to find both areas.