There is a playground measuring 50 m `xx` 30 m . In one corner of the ground , a pit of dimensions 4 m `xx` 3 m `xx` 1 m is dug and the mud is spread all over the ground uniformly What is the approximate height of the layer of mud spread ?

Answer

To solve the problem step by step, we need to find the approximate height of the layer of mud spread uniformly over the playground after digging a pit. Here’s how we can do it:

### Step 1: Calculate the Volume of the Pit
The volume of a cuboid (which is the shape of the pit) is calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]

Given the dimensions of the pit:
- Length = 4 m
- Breadth = 3 m
- Height = 1 m

Substituting the values:
\[ \text{Volume of the pit} = 4 \, \text{m} \times 3 \, \text{m} \times 1 \, \text{m} = 12 \, \text{m}^3 \]

### Step 2: Calculate the Area of the Playground
The area of the rectangular playground can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

Given the dimensions of the playground:
- Length = 50 m
- Breadth = 30 m

Substituting the values:
\[ \text{Area of the playground} = 50 \, \text{m} \times 30 \, \text{m} = 1500 \, \text{m}^2 \]

### Step 3: Calculate the Height of the Layer of Mud
The height of the mud layer spread uniformly over the playground can be calculated using the formula:
\[ \text{Height} = \frac{\text{Volume of mud}}{\text{Area of playground}} \]

Substituting the values:
\[ \text{Height} = \frac{12 \, \text{m}^3}{1500 \, \text{m}^2} \]

Calculating the height:
\[ \text{Height} = \frac{12}{1500} = 0.008 \, \text{m} \]

### Step 4: Convert Height to Millimeters
Since the height is often more practical to express in millimeters, we convert meters to millimeters:
\[ 0.008 \, \text{m} = 0.008 \times 1000 \, \text{mm} = 8 \, \text{mm} \]

### Final Answer
The approximate height of the layer of mud spread uniformly over the playground is **8 mm**.

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