There is a playground measuring 50 m `xx` 30 m . In one corner of the ground , a pit of dimesions 5 m `xx` 4 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 ?

Options

A. 7 mm
B. 8 mm
C. 14 mm
D. 10 mm

Answer

To solve the problem step by step, we need to find the approximate height of the layer of mud that is spread uniformly over the playground after digging a pit.

### Step 1: Calculate the volume of the pit
The dimensions of the pit are given as 5 m x 4 m x 1 m.

**Volume of the pit = Length x Breadth x Height**
\[ \text{Volume of the pit} = 5 \, \text{m} \times 4 \, \text{m} \times 1 \, \text{m} = 20 \, \text{m}^3 \]

**Hint:** Remember that the volume of a rectangular prism (like the pit) is calculated by multiplying its length, breadth, and height.

### Step 2: Calculate the area of the playground
The dimensions of the playground are given as 50 m x 30 m.

**Area of the playground = Length x Breadth**
\[ \text{Area of the playground} = 50 \, \text{m} \times 30 \, \text{m} = 1500 \, \text{m}^2 \]

**Hint:** The area of a rectangle is found by multiplying its length by its width.

### Step 3: Calculate the height of the mud layer
The volume of the mud (which is the same as the volume of the pit) will be spread uniformly over the area of the playground.

**Height of the mud layer = Volume of the mud / Area of the playground**
\[ \text{Height of the mud layer} = \frac{\text{Volume of the pit}}{\text{Area of the playground}} = \frac{20 \, \text{m}^3}{1500 \, \text{m}^2} \]
\[ \text{Height of the mud layer} = \frac{20}{1500} = \frac{2}{150} = \frac{1}{75} \, \text{m} \]

**Hint:** When spreading a volume over an area, the height can be found by dividing the volume by the area.

### Step 4: Convert height from meters to millimeters
Since 1 meter = 1000 millimeters, we need to convert the height from meters to millimeters.

\[ \text{Height in mm} = \frac{1}{75} \, \text{m} \times 1000 \, \text{mm/m} = \frac{1000}{75} \, \text{mm} \]
\[ \text{Height in mm} = 13.33 \, \text{mm} \approx 14 \, \text{mm} \]

**Hint:** To convert meters to millimeters, multiply by 1000.

### Final Answer
The approximate height of the layer of mud spread over the playground is **14 mm**.