Determine the size of "lung" with diameter 7cm. 45cm in a 50cm length of pipe. If the 5cm is given and the pipe length is 50cm. Calculate the mass of the lung.

Eneo $= \frac{1}{2}ab \sin \theta$
Ambapo $a$ na $b$ ni urefu wa pande mbili, na $\theta$ ni pembe iliyoko katikati ya pande hizo.

Tunapewa $AB = 10$ cm, $BC = 12$ cm, na $\angle ABC = 30^\circ$.
Eneo $= \frac{1}{2} \times 10 \text{ cm} \times 12 \text{ cm} \times \sin(30^\circ)$

Tunajua kuwa $\sin(30^\circ) = 0.5$.
Eneo $= \frac{1}{2} \times 10 \times 12 \times 0.5$
Eneo $= 5 \times 12 \times 0.5$
Eneo $= 60 \times 0.5$
Eneo $= 30 \text{ cm}^2$

Eneo la pembetatu ABC ni $\boxed{\text{30 cm}^2}$.

$c^2 = a^2 + b^2 - 2ab \cos C$
Katika kesi hii, tunatafuta $AC$, kwa hivyo:
$AC^2 = AB^2 + BC^2 - 2(AB)(BC) \cos(\angle ABC)$

Tunapewa $AB = 10$ cm, $BC = 12$ cm, na $\angle ABC = 30^\circ$.
$AC^2 = (10 \text{ cm})^2 + (12 \text{ cm})^2 - 2(10 \text{ cm})(12 \text{ cm}) \cos(30^\circ)$

Tunajua kuwa $\cos(30^\circ) = \frac{\sqrt{3}}{2} \approx 0.8660$.
$AC^2 = 100 + 144 - 2(10)(12) \left(\frac{\sqrt{3}}{2}\right)$
$AC^2 = 244 - 240 \left(\frac{\sqrt{3}}{2}\right)$
$AC^2 = 244 - 120\sqrt{3}$
$AC^2 \approx 244 - 120(1.73205)$
$AC^2 \approx 244 - 207.846$
$AC^2 \approx 36.154$

$AC = \sqrt{36.154}$
$AC \approx 6.0128 \text{ cm}$

Urefu wa AC ni $\boxed{\text{6.01 cm}}$ (kwa sehemu mbili za desimali).