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JAMB Mathematics 2012 Paper

Question : 46

Total: 48

Solution:

Concept:

A sector’s area is a fraction of the full circle’s area, based on the ratio of its central angle to

360^{\circ}

Explanation:

The area of a sector is given by:

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

Here,

\theta = 150^{\circ}

and the radius

r = 12 \, \text{cm}

Substituting these values:

A = \frac{150}{360} \times \pi \times (12)^{2}

Simplify

\frac{150}{360}

\frac{5}{12}

A = \frac{5}{12} \times \pi \times 144

Since

144 \div 12 = 12

, we get:

A = 5 \times 12 \times \pi = 60\pi

Thus, the area of the sector is

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

Answer:

The correct option is B:

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

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