NCERT Example 1 — Areas Related to Circles

NCERT Example

Example 1

area of sector · major sector

Find the area of the sector of a circle with radius 4 cm and angle 30°. Also find the area of the corresponding major sector. Use π = 3.14.

Board-exam working:

Given: radius r = 4 cm and central angle θ = 30°.

Area of the minor sector:

A_{minor}=\frac{\theta}{360^\circ}\times\pi r^2

=\frac{30^\circ}{360^\circ}\times3.14\times4^2

=\frac{1}{12}\times3.14\times16

=\frac{12.56}{3}=4.186\ldots\text{ cm}^2

A_{minor}\approx4.19\text{ cm}^2

Area of the whole circle:

\pi r^2=3.14\times4^2=50.24\text{ cm}^2

Therefore, area of the corresponding major sector:

A_{major}=50.24-4.19=46.05\text{ cm}^2

A_{major}\approx46.1\text{ cm}^2

A_{minor}\approx4.19\text{ cm}^2,\qquad A_{major}\approx46.1\text{ cm}^2