A circle of area 9cm² and radius 9cm is mapped onto a sector of area 16cm² and diameter 16cm. Calculate the value of θ.

Radiasi ya duara la kwanza, $r_1 = 9 \text{ cm}$.
Eneo la duara la kwanza, $A_1$, linahesabiwa kwa kutumia fomula $A = \pi r^2$.

$$A_1 = \pi (9 \text{ cm})^2$$ $$A_1 = 81\pi \text{ cm}^2$$

Eneo la duara la pili, $A_2$, limepewa kama $16 \text{ cm}^2$.
Acha $r_2$ iwe radiasi ya duara la pili. Tunajua $A_2 = \pi r_2^2$.

$$16 \text{ cm}^2 = \pi r_2^2$$

Ili kupata $r_2^2$, tunagawanya pande zote mbili kwa $\pi$:

$$r_2^2 = \frac{16}{\pi} \text{ cm}^2$$

Ili kupata $r_2$, tunachukua mzizi wa mraba wa pande zote mbili:

$$r_2 = \sqrt{\frac{16}{\pi}} \text{ cm}$$ $$r_2 = \frac{4}{\sqrt{\pi}} \text{ cm}$$

Kipenyo $d$ ni mara mbili ya radiasi $r_2$.

$$d = 2 r_2$$ $$d = 2 \times \frac{4}{\sqrt{\pi}} \text{ cm}$$ $$d = \frac{8}{\sqrt{\pi}} \text{ cm}$$

Thamani ya $d$ ni:

$$\boxed{\frac{8}{\sqrt{\pi}} \text{ cm}}$$

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