The floor of a room is of dimensions 5m `xx` 4m and it is covered with circular tiles of diameters 50 cm each. Find the area of the floor that remains uncovered with tiles. (Use `pi` = 3.14)

Answer

To find the area of the floor that remains uncovered with circular tiles, we can follow these steps:

### Step 1: Calculate the area of the floor
The dimensions of the floor are given as 5 meters by 4 meters. The area of a rectangle is calculated using the formula:

\[ \text{Area of the floor} = \text{Length} \times \text{Breadth} \]

Substituting the values:

\[ \text{Area of the floor} = 5 \, \text{m} \times 4 \, \text{m} = 20 \, \text{m}^2 \]

### Step 2: Convert the diameter of the tiles to meters
The diameter of each circular tile is given as 50 cm. To convert this to meters:

\[ \text{Diameter} = 50 \, \text{cm} = \frac{50}{100} \, \text{m} = 0.5 \, \text{m} \]

### Step 3: Calculate the radius of the tiles
The radius \( r \) of the circular tile is half of the diameter:

\[ r = \frac{\text{Diameter}}{2} = \frac{0.5}{2} = 0.25 \, \text{m} \]

### Step 4: Calculate the area of one tile
The area \( A \) of a circle is calculated using the formula:

\[ A = \pi r^2 \]

Substituting the values (using \( \pi = 3.14 \)):

\[ A = 3.14 \times (0.25)^2 = 3.14 \times 0.0625 = 0.19625 \, \text{m}^2 \]

### Step 5: Calculate the number of tiles that fit in the floor
To find how many tiles fit along the length and breadth of the floor, we divide the dimensions of the floor by the diameter of the tiles:

\[ \text{Number of tiles along length} = \frac{5 \, \text{m}}{0.5 \, \text{m}} = 10 \]

\[ \text{Number of tiles along breadth} = \frac{4 \, \text{m}}{0.5 \, \text{m}} = 8 \]

### Step 6: Calculate the total number of tiles
The total number of tiles is the product of the number of tiles along the length and the breadth:

\[ \text{Total tiles} = 10 \times 8 = 80 \]

### Step 7: Calculate the total area covered by the tiles
Now, we can find the total area covered by all the tiles:

\[ \text{Total area covered by tiles} = \text{Total tiles} \times \text{Area of one tile} \]

Substituting the values:

\[ \text{Total area covered by tiles} = 80 \times 0.19625 = 15.7 \, \text{m}^2 \]

### Step 8: Calculate the uncovered area
Finally, we can find the area of the floor that remains uncovered by subtracting the area covered by the tiles from the total area of the floor:

\[ \text{Uncovered area} = \text{Area of the floor} - \text{Total area covered by tiles} \]

Substituting the values:

\[ \text{Uncovered area} = 20 \, \text{m}^2 - 15.7 \, \text{m}^2 = 4.3 \, \text{m}^2 \]

### Final Answer
The area of the floor that remains uncovered with tiles is:

\[ \boxed{4.3 \, \text{m}^2} \]

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