A rectangular tank measuring $5 \text{ m} \times 4.5 \text{ m} \times 2.1 \text{ m}$ is dug in the centre of the field measuring $13.5 \text{ m}$ by $2.5 \text{ m}$. The earth dug out is evenly spread over the remaining portion of the field. How much is the level of the field raised?

### Concept & Formula To find the rise in the level of the field, we need to divide the volume of the earth dug out by the area of the remaining field over which it is spread. $$ \text{Rise in level} = \frac{\text{Volume of earth dug out}}{\text{Total area of field} - \text{Area of tank base}} $$ ### Step-by-Step Solution 1. **Find the volume of earth dug out:** $\text{Volume} = 5 \text{ m} \times 4.5 \text{ m} \times 2.1 \text{ m} = 47.25 \text{ m}^3$ 2. **Find the total area of the field:** $\text{Area} = 13.5 \text{ m} \times 2.5 \text{ m} = 33.75 \text{ m}^2$ 3. **Find the base area of the dug tank:** $\text{Tank Area} = 5 \text{ m} \times 4.5 \text{ m} = 22.5 \text{ m}^2$ 4. **Calculate the remaining area where earth is spread:** $\text{Remaining Area} = 33.75 - 22.5 = 11.25 \text{ m}^2$ 5. **Calculate the rise in level:** $\text{Rise} = \frac{47.25}{11.25} = 4.2 \text{ m}$ ### Exam Strategy & Shortcut Work with fractions to simplify calculations: $47.25 / 11.25 = \frac{189/4}{45/4} = \frac{189}{45} = \frac{21}{5} = 4.2$. ### Common Pitfall Spreading the earth over the *entire* field area instead of subtracting the area of the dug tank first. ### Final Answer Therefore, the correct answer is **4.2 m**.