A milk container is 8 cm long and 50 cm wide. The height of the container, so that it can hold 4 litres of milk is `k` cm. The value of `k` is

Answer

To find the height \( k \) of the milk container that can hold 4 litres of milk, we will follow these steps:

### Step 1: Understand the dimensions of the container
The container is a cuboid with:
- Length \( L = 8 \) cm
- Breadth \( B = 50 \) cm

### Step 2: Convert litres to cubic centimeters
We know that:
- 1 litre = 1000 cm³
Thus, for 4 litres:
\[ 4 \text{ litres} = 4 \times 1000 \text{ cm}^3 = 4000 \text{ cm}^3 \]

### Step 3: Use the formula for the volume of a cuboid
The volume \( V \) of a cuboidal container is given by the formula:
\[ V = L \times B \times H \]
Where \( H \) is the height of the container.

### Step 4: Set up the equation
We know the volume \( V \) is 4000 cm³, so we can set up the equation:
\[ 4000 = 8 \times 50 \times H \]

### Step 5: Solve for \( H \)
First, calculate \( 8 \times 50 \):
\[ 8 \times 50 = 400 \]
Now substitute this back into the equation:
\[ 4000 = 400 \times H \]
To find \( H \), divide both sides by 400:
\[ H = \frac{4000}{400} = 10 \text{ cm} \]

### Step 6: Conclusion
Thus, the height \( k \) of the container is:
\[ k = 10 \text{ cm} \]

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