A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 22 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the rise in level of the field will be---

Options

A. 0.299 cm
B. 0.29 cm
C. 2.98 cm
D. 4.15 cm

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the volume of the tank
The volume of the tank can be calculated using the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Depth} \]
Given:
- Length of the tank = 3 m
- Width of the tank = 2 m
- Depth of the tank = 1.5 m

Calculating the volume:
\[ \text{Volume} = 3 \, \text{m} \times 2 \, \text{m} \times 1.5 \, \text{m} = 9 \, \text{m}^3 \]

### Step 2: Calculate the area of the field
The area of the field can be calculated using the formula for the area of a rectangle:
\[ \text{Area} = \text{Length} \times \text{Width} \]
Given:
- Length of the field = 22 m
- Width of the field = 14 m

Calculating the area:
\[ \text{Area} = 22 \, \text{m} \times 14 \, \text{m} = 308 \, \text{m}^2 \]

### Step 3: Calculate the rise in level of the field
The earth dug out from the tank will be spread evenly over the area of the field. We need to find the rise in level, which can be calculated using the formula:
\[ \text{Rise in Level} = \frac{\text{Volume of Earth}}{\text{Area of Field}} \]

Substituting the values:
\[ \text{Rise in Level} = \frac{9 \, \text{m}^3}{308 \, \text{m}^2} \]

Calculating the rise in level:
\[ \text{Rise in Level} = \frac{9}{308} \approx 0.02922 \, \text{m} \]

### Step 4: Convert the rise in level to centimeters
Since the answer is required in centimeters, we convert meters to centimeters (1 m = 100 cm):
\[ \text{Rise in Level in cm} = 0.02922 \, \text{m} \times 100 = 2.922 \, \text{cm} \]

### Final Answer
The rise in level of the field will be approximately **2.92 cm**.

---