A chord of a circle subtends an angle of 120° at the centre of a circle of diameter 4{3}\,{cm}. Calculate the area of the major sector.

Correct Answer is : 8πππ cm2²2

Correct Answer is : 8πππ cm2²2

Test Index

JAMB Mathematics 2013 Paper

Question : 40

Total: 47

4\sqrt{3}\,\text{cm}

. Calculate the area of the major sector.

Solution:

Concept:

The major sector is the larger portion of the circle left after removing the minor sector of

120^\circ

. Its area is found using the sector area formula with the major angle.

Explanation:

The diameter is

4\sqrt{3}\,\text{cm}

, so the radius is:

r = \frac{4\sqrt{3}}{2} = 2\sqrt{3}\,\text{cm}

The major sector angle is:

360^\circ - 120^\circ = 240^\circ

Area of a sector is:

\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2

Substitute

\theta = 240^\circ

and

r = 2\sqrt{3}

\text{Area} = \frac{240}{360} \times \pi \times (2\sqrt{3})^2

Since

(2\sqrt{3})^2 = 4 \times 3 = 12

\text{Area} = \frac{2}{3} \times \pi \times 12 = 8\pi\,\text{cm}^2

Answer:

8\pi\,\text{cm}^2

, which is option C.

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