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Mathematics · Areas Related to Circles · NCERT Examples

Example 1

A complete, independently verified solution for NCERT Example 1.

Mathematics · Chapter 11 · NCERT Examples

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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.

Circle with centre O, radius 4 centimetres and a 30 degree minor sector OAPB.
Figure 11-5 from the supplied NCERT chapter.

Solution

Board-exam working:

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

Area of the minor sector:

Aminor=θ360∘×πr2A_{minor}=\frac{\theta}{360^\circ}\times\pi r^2
=30∘360∘×3.14×42=\frac{30^\circ}{360^\circ}\times3.14\times4^2
=112×3.14×16=\frac{1}{12}\times3.14\times16
=12.563=4.186… cm2=\frac{12.56}{3}=4.186\ldots\text{ cm}^2
Aminor≈4.19 cm2A_{minor}\approx4.19\text{ cm}^2

Area of the whole circle:

πr2=3.14×42=50.24 cm2\pi r^2=3.14\times4^2=50.24\text{ cm}^2

Therefore, area of the corresponding major sector:

Amajor=50.24−4.19=46.05 cm2A_{major}=50.24-4.19=46.05\text{ cm}^2
Amajor≈46.1 cm2A_{major}\approx46.1\text{ cm}^2

Final answer

Aminor≈4.19 cm2,Amajor≈46.1 cm2A_{minor}\approx4.19\text{ cm}^2,\qquad A_{major}\approx46.1\text{ cm}^2