A cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm. What is the total area of the wet surface inside the cistern in square metres?

Introduction / Context:
This question is about the concept of wet surface area in a container partially filled with water. It tests whether you can distinguish between the surfaces that are in contact with water and those that are dry, and then compute the total area of those wetted surfaces. This is a practical application of surface area of cuboids in mensuration.

Given Data / Assumptions:

- The cistern is rectangular with length 6 m and width 4 m.
- Water depth is 1 m 25 cm, which is 1.25 m.
- The bottom of the cistern is fully covered by water.
- The water wets the side walls up to a height of 1.25 m from the bottom.
- We need the total area of all surfaces in contact with water in square metres.

Concept / Approach:
The wet surface includes the base area and the area of the vertical sides up to the water level. The top horizontal surface at the water level is not part of the wall or bottom, so it is not counted as surface area; it is simply the water surface. For a rectangular cistern, opposite walls are equal, and we can group them for easier calculation.

Step-by-Step Solution:
Step 1: Convert the depth to metres: 1 m 25 cm = 1.25 m.Step 2: Bottom wet area = length * width = 6 * 4 = 24 sq. m.Step 3: Two longer side walls each have dimensions 6 m by 1.25 m. Combined area of these walls = 2 * (6 * 1.25) = 2 * 7.5 = 15 sq. m.Step 4: The other two side walls each have dimensions 4 m by 1.25 m. Combined area of these walls = 2 * (4 * 1.25) = 2 * 5 = 10 sq. m.Step 5: Total wet surface area = bottom area + area of all four wetted walls = 24 + 15 + 10.Step 6: 24 + 15 + 10 = 49 sq. m.

Verification / Alternative check:
As a quick check, note that the total side area up to the water line should equal perimeter of the base multiplied by depth. Perimeter of base = 2 * (6 + 4) = 20 m. Side area up to water level = 20 * 1.25 = 25 sq. m. This equals 15 + 10 from the individual wall calculation, confirming the side area is correct. Adding the bottom area 24 gives 24 + 25 = 49 sq. m again.

Why Other Options Are Wrong:
50, 51, 52 and 55 sq. m all result from small miscalculations, often caused by rounding or by mistakenly adding the water surface at the top. They may also occur if a student includes the total tank height instead of the actual water depth or omits one pair of walls when computing the wetted area.

Common Pitfalls:
A frequent error is to calculate the total surface area of the cistern, including dry portions, instead of only the wetted surfaces. Another mistake is failing to convert 1 m 25 cm correctly into 1.25 m, or forgetting that there are two walls of each type. Careful identification of which surfaces actually touch water and accurate unit conversion are essential to avoid these mistakes.

Final Answer:
The total area of the wet surface inside the cistern is 49 sq. m.