1. **State the problem:** We are given a rectangular tank and need to verify the total surface area (T.S.A) calculation, calculate the volume, and find the height of water when 40 liters are in the tank. 2. **Total Surface Area (T.S.A) of a cylinder formula:** $$\text{T.S.A} = 2 \pi r^2 + 2 \pi r H$$ where $r$ is the radius and $H$ is the height. 3. **Given values:** - Radius $r = 9$ cm - Height $H = 120$ cm 4. **Calculate T.S.A:** $$\text{T.S.A} = 2 \times \pi \times 9^2 + 2 \times \pi \times 9 \times 120$$ $$= 2 \times \pi \times 81 + 2 \times \pi \times 1080$$ $$= 162\pi + 2160\pi = 2322\pi$$ 5. **Approximate using $\pi \approx 3.14$:** $$2322 \times 3.14 = 7289.08 \text{ cm}^2$$ 6. **Note:** The original problem's T.S.A calculation seems inconsistent with the formula and values given. The correct T.S.A for a cylinder with $r=9$ cm and $H=120$ cm is approximately $7289.08$ cm$^2$. 7. **Calculate volume of the tank (rectangular prism):** $$\text{Volume} = L \times W \times H$$ Given: - Length $L = 50$ cm - Width $W = 110$ cm - Height $H = 30$ cm $$\text{Volume} = 50 \times 110 \times 30 = 165000 \text{ cm}^3$$ 8. **Convert 40 liters to cm$^3$:** Since 1 liter = 1000 cm$^3$, 40 liters = 40000 cm$^3$. 9. **Calculate height of water in the tank:** Using volume formula for rectangular prism: $$\text{Volume} = L \times W \times h$$ where $h$ is the height of water. Rearranged: $$h = \frac{\text{Volume}}{L \times W} = \frac{40000}{50 \times 110} = \frac{40000}{5500} = 7.27 \text{ cm}$$ **Final answers:** - Total Surface Area (cylinder) $\approx 7289.08$ cm$^2$ - Volume of tank $= 165000$ cm$^3$ - Height of water $= 7.27$ cm