A cistern 6 metres long and 4 metres wide contains water up to a height of 1 metre 25cm. Find the total area of the wet surface.

Options

A. `42 m^2`
B. `49 m^2`
C. `52 m^2`
D. `64 m^2`

Answer

To find the total area of the wet surface of the cistern, we need to calculate the area of the four walls and the base that is in contact with the water.

### Step-by-Step Solution:

1. **Convert Height to Meters:**
- The height of the water is given as 1 meter 25 centimeters.
- Convert this to meters:
\[ 1 \text{ m} + 25 \text{ cm} = 1 \text{ m} + 0.25 \text{ m} = 1.25 \text{ m} \]

2. **Identify the Dimensions of the Cistern:**
- Length (L) = 6 meters
- Width (W) = 4 meters
- Height of water (H) = 1.25 meters

3. **Calculate the Area of the Four Walls:**
- The area of the two longer walls (length x height):
\[ \text{Area of two longer walls} = 2 \times (L \times H) = 2 \times (6 \times 1.25) = 2 \times 7.5 = 15 \text{ m}^2 \]
- The area of the two shorter walls (width x height):
\[ \text{Area of two shorter walls} = 2 \times (W \times H) = 2 \times (4 \times 1.25) = 2 \times 5 = 10 \text{ m}^2 \]

4. **Calculate the Total Area of the Walls:**
- Total area of the walls:
\[ \text{Total area of walls} = 15 + 10 = 25 \text{ m}^2 \]

5. **Calculate the Area of the Base:**
- The area of the base (length x width):
\[ \text{Area of the base} = L \times W = 6 \times 4 = 24 \text{ m}^2 \]

6. **Calculate the Total Wet Surface Area:**
- Total wet surface area = Area of the walls + Area of the base:
\[ \text{Total wet surface area} = 25 + 24 = 49 \text{ m}^2 \]

### Final Answer:
The total area of the wet surface is **49 m²**.