Tank Water Volume Fd40Ec

1. **State the problem:** We have three rectangular tanks A, B, and C. Tank A is initially filled to 3/5 of its height with water. Water flows from tank A to tank B, then to tank C, and finally 3 liters overflow from tank C. We need to find how much water tank A contained at first in litres and millilitres. 2. **Identify dimensions and volumes:** - Tank A dimensions: base area unknown, height = 45 cm - Tank B dimensions: 25 cm × 22 cm × 14 cm - Tank C dimensions: 22 cm × 15 cm × 12 cm 3. **Calculate volume of water initially in tank A:** - Height of water in tank A = $\frac{3}{5} \times 45 = 27$ cm - Base area of tank A is not given explicitly, but we can find it by using the volumes of tanks B and C and the overflow. 4. **Calculate volumes of tanks B and C:** - Volume of tank B = $25 \times 22 \times 14 = 7700$ cm$^3$ - Volume of tank C = $22 \times 15 \times 12 = 3960$ cm$^3$ 5. **Convert overflow volume to cm$^3$:** - $3$ litres = $3000$ cm$^3$ 6. **Total volume of water after flow:** - Water fills tank B completely (since it was empty), volume = 7700 cm$^3$ - Water fills tank C completely plus 3 litres overflow, so water volume in C before overflow = $3960 + 3000 = 6960$ cm$^3$ 7. **Total water volume initially in tank A:** - Total water = volume in B + volume in C before overflow - $7700 + 6960 = 14660$ cm$^3$ 8. **Calculate base area of tank A:** - Volume of water in tank A initially = base area $\times$ height of water - Let base area = $A$ cm$^2$ - $A \times 27 = 14660$ - $A = \frac{14660}{27} \approx 542.96$ cm$^2$ 9. **Calculate total volume of tank A:** - Total volume = base area $\times$ total height = $542.96 \times 45 = 24433.2$ cm$^3$ 10. **Convert initial water volume to litres and millilitres:** - $14660$ cm$^3$ = $14.66$ litres = $14$ litres and $660$ millilitres **Final answer:** Tank A initially contained **14 litres and 660 millilitres** of water.