A tank 4m long and 2.5 m wide and 6 m deep is dug in a field 10 m long and 9 m wide. If the earth dugout is evenly spread over the field , the rise in level of the field will be :

Options

A. 80 cm
B. 75 cm
C. 60 cm
D. 30 cm

Answer

To solve the problem, we need to find the rise in the level of the field after the earth dug out from the tank is spread evenly over the field.

### Step-by-Step Solution:

1. **Calculate the Volume of the Tank:**
The tank is in the shape of a cuboid. The formula for the volume \( V \) of a cuboid is given by:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
Given:
- Length of the tank \( L = 4 \, \text{m} \)
- Breadth of the tank \( B = 2.5 \, \text{m} \)
- Height of the tank \( H = 6 \, \text{m} \)

Substituting the values:
\[ V = 4 \times 2.5 \times 6 = 60 \, \text{m}^3 \]

2. **Calculate the Area of the Field:**
The field is also in the shape of a rectangle. The area \( A \) of a rectangle is given by:
\[ A = \text{Length} \times \text{Width} \]
Given:
- Length of the field \( L_f = 10 \, \text{m} \)
- Width of the field \( W_f = 9 \, \text{m} \)

Substituting the values:
\[ A = 10 \times 9 = 90 \, \text{m}^2 \]

3. **Calculate the Rise in Level of the Field:**
The rise in level \( h \) can be calculated by dividing the volume of the earth dug out by the area of the field:
\[ h = \frac{V}{A} \]
Substituting the values:
\[ h = \frac{60 \, \text{m}^3}{90 \, \text{m}^2} = \frac{60}{90} = \frac{2}{3} \, \text{m} \]

4. **Convert the Rise in Level to Centimeters:**
Since 1 meter = 100 centimeters, we convert the rise in level:
\[ h = \frac{2}{3} \, \text{m} \times 100 = \frac{200}{3} \approx 66.67 \, \text{cm} \]

### Final Answer:
The rise in level of the field will be approximately \( 66.67 \, \text{cm} \).

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