The capacity of a cuboidal water tank is 1,00,000 litres. If its length is 5 m and breadth is 4 m, find its height.

Answer

To find the height of the cuboidal water tank, we can follow these steps:

### Step 1: Understand the given information
We know that:
- The capacity (volume) of the tank is 1,00,000 litres.
- The length of the tank is 5 meters.
- The breadth of the tank is 4 meters.

### Step 2: Convert the volume from litres to cubic meters
Since 1 litre is equal to \( \frac{1}{1000} \) cubic meters, we can convert 1,00,000 litres to cubic meters:
\[ \text{Volume in cubic meters} = 1,00,000 \text{ litres} \times \frac{1 \text{ m}^3}{1000 \text{ litres}} = 100 \text{ m}^3 \]

### Step 3: Use the formula for the volume of a cuboid
The formula for the volume \( V \) of a cuboid is given by:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
We can rearrange this formula to solve for height:
\[ \text{Height} = \frac{V}{\text{Length} \times \text{Breadth}} \]

### Step 4: Substitute the known values into the formula
Substituting the known values into the rearranged formula:
\[ \text{Height} = \frac{100 \text{ m}^3}{5 \text{ m} \times 4 \text{ m}} = \frac{100 \text{ m}^3}{20 \text{ m}^2} \]

### Step 5: Calculate the height
Now, we can calculate the height:
\[ \text{Height} = \frac{100}{20} = 5 \text{ m} \]

### Final Answer
The height of the cuboidal water tank is **5 meters**.

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