A cuboidal shaped water tank, 2.1 m long ans 1.5 broad is hald filled with water. If 630 liters more half is poured into that tank, the water level will rise

Options

A. 0.15 cm
B. 0.20 metre
C. 0.18 cm
D. 2 cm

Answer

To solve the problem step by step, we need to find out how much the water level rises in the cuboidal tank after pouring in an additional 630 liters of water.

### Step-by-Step Solution:

1. **Identify the dimensions of the tank:**
- Length (L) = 2.1 m
- Breadth (B) = 1.5 m

2. **Calculate the volume of water already in the tank:**
- Since the tank is half-filled, we need to find the volume of the tank when it is full first.
- The volume (V) of a cuboid is given by the formula:
\[ V = L \times B \times H \]
- However, we don't have the height (H) of the tank yet. We will calculate the height later.

3. **Convert the additional water volume from liters to cubic meters:**
- We know that 1 liter = 0.001 cubic meters.
- Therefore, 630 liters = \( 630 \times 0.001 = 0.63 \) m³.

4. **Calculate the total volume of water after pouring in the additional water:**
- Since the tank is half-filled, we can denote the volume of water already in the tank as \( \frac{V}{2} \).
- The new total volume of water in the tank will be:
\[ \text{Total Volume} = \frac{V}{2} + 0.63 \]

5. **Calculate the height of the water in the tank:**
- The volume of the tank when full is:
\[ V = L \times B \times H = 2.1 \times 1.5 \times H \]
- Since the tank is half-filled, the volume of water currently in the tank is:
\[ \frac{V}{2} = \frac{2.1 \times 1.5 \times H}{2} \]
- Setting this equal to the volume of water we have:
\[ \frac{2.1 \times 1.5 \times H}{2} + 0.63 = \frac{2.1 \times 1.5 \times H + 1.26}{2} \]

6. **Calculate the height of the water level after pouring in the additional water:**
- The total volume of water in the tank after pouring in the additional water is:
\[ \frac{2.1 \times 1.5 \times H + 1.26}{2} \]
- To find the new height (h) of the water, we can use the volume formula again:
\[ V = L \times B \times h \]
- Rearranging gives:
\[ h = \frac{\text{Total Volume}}{L \times B} \]
- Substituting the values:
\[ h = \frac{(2.1 \times 1.5 \times H + 1.26)}{2.1 \times 1.5} \]

7. **Calculate the rise in water level:**
- The rise in water level is given by:
\[ \text{Rise} = h - \frac{H}{2} \]
- After calculating, we find that the rise in water level is 0.2 m.

### Final Answer:
The water level will rise by 0.2 meters.