Introduction / Context:
This is a classic cistern or tank problem from mensuration. The wet surface area means the total area of the surfaces that are in contact with water. For an open rectangular cistern partly filled with water, the wet surface usually includes the bottom and the vertical walls up to the water level. Understanding which surfaces are wet and calculating their areas correctly is essential for solving this type of question.
Given Data / Assumptions:
- Length of cistern, L = 6 m.
- Breadth of cistern, B = 4 m.
- Water depth, h = 1 m 25 cm = 1.25 m.
- The cistern is open at the top.
- Wet surfaces are the bottom and the four vertical walls up to height h.
Concept / Approach:
The wet surface area A wet is the sum of:
- Area of bottom = L * B.
- Area of two longer side walls = 2 * (L * h).
- Area of two shorter side walls = 2 * (B * h).
Therefore:
A wet = L * B + 2 * L * h + 2 * B * h
We simply substitute the given values and compute.
Step-by-Step Solution:
Step 1: Compute area of bottom.
Bottom area = L * B = 6 * 4 = 24 square metres.
Step 2: Compute area of two longer side walls.
One long wall area = L * h = 6 * 1.25 = 7.5 square metres.
Two long walls area = 2 * 7.5 = 15 square metres.
Step 3: Compute area of two shorter side walls.
One short wall area = B * h = 4 * 1.25 = 5 square metres.
Two short walls area = 2 * 5 = 10 square metres.
Step 4: Sum all wet surfaces.
Total wet area = bottom + long walls + short walls
Total wet area = 24 + 15 + 10 = 49 square metres.
Thus, the total wet surface area is 49 square metres.
Verification / Alternative check:
We can rewrite the formula in a compact form: A wet = L * B + 2 * h * (L + B). Substituting L = 6, B = 4, h = 1.25: L + B = 10, 2 * h * (L + B) = 2 * 1.25 * 10 = 25, and bottom area is 24. Therefore total area = 24 + 25 = 49 square metres, confirming our earlier calculation.
Why Other Options Are Wrong:
Option B (50) and Option C (53.5) are close but incorrect, likely stemming from rounding or arithmetic mistakes when multiplying or adding wall areas. Option D (55) arises if the depth is taken incorrectly or if an extra surface is mistakenly included. Option E (45) indicates that one or more surfaces, such as either pair of walls or the bottom, were omitted.
Common Pitfalls:
Students often forget to convert mixed units like 1 m 25 cm fully into metres. Another common error is to include the top surface, which is not in contact with water, or to miss one pair of walls. Being systematic about which surfaces are actually in contact with water avoids these mistakes.
Final Answer:
The total area of the wet surface of the cistern is
49 square metres.
Discussion & Comments