To find the cost of flooring a room that measures 7.5 meters by 6 meters with square tiles that have a side length of 30 centimeters, at a rate of 6 per tile, we'll need to proceed with the following calculations:
1. Dimensions of the Room:
- The length of the room is 7.5 meters.
- The width of the room is 6 meters.
2. Area of the Room:
- The area of the room can be calculated by multiplying the length and the width:
[tex]\[
\text{Area of the room} = 7.5 \text{ meters} \times 6 \text{ meters} = 45.0 \text{ square meters}
\][/tex]
3. Dimensions of Each Tile:
- Each tile has a side length of 30 centimeters.
- Since there are 100 centimeters in a meter, 30 centimeters is:
[tex]\[
30 \text{ centimeters} = 0.3 \text{ meters}
\][/tex]
4. Area of Each Tile:
- The area of each tile is the side length squared:
[tex]\[
\text{Area of each tile} = 0.3 \text{ meters} \times 0.3 \text{ meters} = 0.09 \text{ square meters}
\][/tex]
5. Number of Tiles Needed:
- To find the number of tiles needed, we divide the area of the room by the area of each tile:
[tex]\[
\text{Number of tiles needed} = \frac{\text{Area of the room}}{\text{Area of each tile}} = \frac{45.0 \text{ square meters}}{0.09 \text{ square meters}} = 500 \text{ tiles}
\][/tex]
- Since you cannot have a fraction of a tile, we would round up to the nearest whole number, but in this case, it is already a whole number.
6. Cost Per Tile:
- The cost per tile is given as 6.
7. Total Cost:
- The total cost is the number of tiles multiplied by the cost per tile:
[tex]\[
\text{Total cost} = 500 \text{ tiles} \times 6 \text{ per tile} = 3000
\][/tex]
Therefore, the cost of flooring the room with the given tiles is 3000.
