A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is :

Options

A. 1m
B. 1.1 m
C. 1 dm
D. 90 cm

Answer

To find the thickness of the bottom of the cistern, we will follow these steps:

### Step 1: Convert the capacity from liters to cubic meters.
The capacity of the cistern is given as 8000 liters. Since 1 cubic meter is equal to 1000 liters, we can convert the capacity as follows:
\[ \text{Capacity in cubic meters} = \frac{8000 \text{ liters}}{1000} = 8 \text{ cubic meters} \]

### Step 2: Identify the external dimensions of the cistern.
The external dimensions of the cistern are given as:
- Length (L) = 3.3 m
- Breadth (B) = 2.6 m
- Height (H) = 1.1 m

### Step 3: Calculate the internal dimensions.
The walls of the cistern are 5 cm thick. We need to convert this thickness into meters:
\[ \text{Thickness} = 5 \text{ cm} = 0.05 \text{ m} \]
Now, we will subtract twice the thickness (for both sides) from the external dimensions to find the internal dimensions:
- Internal Length = \(3.3 - 2 \times 0.05 = 3.3 - 0.1 = 3.2 \text{ m}\)
- Internal Breadth = \(2.6 - 2 \times 0.05 = 2.6 - 0.1 = 2.5 \text{ m}\)

### Step 4: Set up the equation for the internal volume.
The internal volume of the cistern can be expressed as:
\[ \text{Internal Volume} = \text{Internal Length} \times \text{Internal Breadth} \times \text{Internal Height} \]
Let the internal height be \(h\). Then:
\[ 3.2 \times 2.5 \times h = 8 \]

### Step 5: Solve for the internal height \(h\).
Calculating the product of the internal length and breadth:
\[ 3.2 \times 2.5 = 8 \]
So, we have:
\[ 8 \times h = 8 \]
Dividing both sides by 8 gives:
\[ h = 1 \text{ m} \]

### Step 6: Calculate the thickness of the bottom.
The external height of the cistern is 1.1 m. Since we found the internal height to be 1 m, the thickness of the bottom can be calculated as:
\[ \text{Thickness of the bottom} = \text{External Height} - \text{Internal Height} = 1.1 - 1 = 0.1 \text{ m} \]
Converting this to centimeters:
\[ 0.1 \text{ m} = 10 \text{ cm} \]

### Final Answer:
The thickness of the bottom of the cistern is **10 cm**.

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