A cistern has a capacity of 8000 litres and its external dimensions are 3.3 m × 2.6 m × 1.1 m. The thickness of each of the four vertical walls is 5 cm. Assuming the top is open, what is the thickness (in centimetres) of the bottom slab of the cistern?

Introduction / Context:
In this aptitude question on volume and surface area, we are dealing with a rectangular cistern (tank) whose external dimensions and wall thickness are known. We are also given its internal capacity in litres. The goal is to determine the thickness of the bottom slab. This type of question tests understanding of the relationship between internal and external dimensions, unit conversion between litres and cubic centimetres, and basic volume formulas for cuboids.

Given Data / Assumptions:

• Capacity of the cistern = 8000 litres.
• External dimensions: length = 3.3 m, breadth = 2.6 m, height = 1.1 m.
• Thickness of each vertical wall = 5 cm.
• Cistern is open at the top, so only the bottom slab thickness reduces the internal height.
• 1 litre = 1000 cubic centimetres.

Concept / Approach:
To find the bottom thickness, first convert everything into centimetres. Then compute the internal length and internal breadth by subtracting twice the wall thickness from the external dimensions. Let the bottom thickness be t cm. The internal height will then be (external height − t). The volume of the inner hollow region must be equal to the given capacity, converted into cubic centimetres. We then solve the resulting linear equation for t.

Step-by-Step Solution:
Convert external dimensions to cm: 3.3 m = 330 cm, 2.6 m = 260 cm, 1.1 m = 110 cm. Internal length = 330 − 2 * 5 = 320 cm. Internal breadth = 260 − 2 * 5 = 250 cm. Let bottom thickness be t cm, so internal height = 110 − t cm. Capacity = 8000 litres = 8000 * 1000 = 8000000 cm^3. Volume of cistern interior = 320 * 250 * (110 − t). So 320 * 250 * (110 − t) = 8000000. 320 * 250 = 80000, so 80000 * (110 − t) = 8000000. Divide both sides by 80000: 110 − t = 100. Therefore t = 110 − 100 = 10 cm.

Verification / Alternative check:
Substitute t = 10 cm back: internal height = 100 cm. Then interior volume = 320 * 250 * 100 = 8000000 cm^3, which equals 8000 litres. This confirms that the computed bottom thickness is consistent with the given capacity of the cistern.

Why Other Options Are Wrong:
5 cm would give internal height 105 cm and a larger volume than 8000 litres. 15 cm and 20 cm would give smaller internal heights and capacities less than 8000 litres. 90 cm is far too large as a bottom thickness and is unrealistic for this geometry, so only 10 cm satisfies the volume condition exactly.

Common Pitfalls:
A common mistake is to forget to convert litres into cubic centimetres or to subtract the wall thickness from both sides when finding internal length and breadth. Another frequent error is to subtract the wall thickness from the height twice, even though there is only one bottom slab and the top is open. Some students also try to use metres for some dimensions and centimetres for others, which leads to unit inconsistency and wrong answers.

Final Answer:
Thus, the thickness of the bottom slab of the cistern is 10 cm.