The area of a sector circle is 63cm. Calculate the angle at the centre of the circle.

Fomula ya eneo la sekta ya duara ni:

$$\text{Eneo} = \frac{\theta}{360^\circ} \pi r^2$$

Tunapewa:

• Eneo la sekta $= 4158 \text{ cm}^2$
• Radiasi $r = 63 \text{ cm}$
• Tumia $\pi = \frac{22}{7}$

Badilisha thamani hizi kwenye fomula:

$$4158 = \frac{\theta}{360^\circ} \times \frac{22}{7} \times (63)^2$$

$$4158 = \frac{\theta}{360^\circ} \times \frac{22}{7} \times 63 \times 63$$

Gawanya 63 kwa 7:

$$4158 = \frac{\theta}{360^\circ} \times 22 \times 9 \times 63$$

Fanya kuzidisha:

$$4158 = \frac{\theta}{360^\circ} \times 198 \times 63$$ $$4158 = \frac{\theta}{360^\circ} \times 12474$$

Ili kupata $\theta$, zidisha pande zote mbili kwa $360^\circ$ na kisha ugawanye kwa 12474:

$$\theta = \frac{4158 \times 360^\circ}{12474}$$ $$\theta = \frac{1496880^\circ}{12474}$$ $$\theta = 120^\circ$$

Pembe inayoundwa katikati ya duara ni $\text{120}^\circ$.