Question

A chord AB of a circle of radius 14 cm makes an angle 90  at the centre of the circle. Find the area of the minor sector.
1. 154 cm²
2. 148 cm²
3. 150 cm²
4. 156 cm²
5. 160 cm²

Answer 1

Correct Answer - Option 1 : 154 cm²

Given:

Radius of chord AB of circle = 14 cm

Angle at the centre of the circle = 90

Concept:

Simply we used the concept of area of the sector.

Formula Used:

Area of sector = \(\frac{\theta }{{360}} \times \;\pi {r^2}\)

Calculation:

Area of minor sector = \(\frac{{90^\circ }}{{360^\circ }}\; \times \;\frac{{22}}{7}\; \times {14^2}\)

⇒ Area of minor sector = \(\frac{{90^\circ }}{{360^\circ }}\; \times \;\frac{{22}}{7}\; \times {14^2}\)

⇒ Area of minor sector = 154 cm²

∴ Area of minor sector is 154 cm²