Sure! Let's break down the problem into the four points you specified:
1. What is this problem all about?
This problem is about figuring out how many square tiles, each measuring 20 cm by 20 cm, are required to cover the sides and the base of a swimming pool. The pool has specific dimensions: it is 10 meters long, 6 meters wide, and 3 meters deep. We need to calculate the total surface area that will be covered by the tiles.
2. What do I know?
- The swimming pool has the following dimensions:
- Length = 10 meters
- Width (or breadth) = 6 meters
- Depth (or height) = 3 meters
- Each tile has dimensions of 20 cm x 20 cm.
- We need to cover both the sides (walls) and the base of the pool with these tiles.
3. What do I need to know more about?
To solve this problem, we need to know:
- How to calculate the total surface area of the pool that needs to be covered.
- How to convert the tile measurements from centimeters to meters so they can be easily compared with the pool dimensions.
- How to calculate how many tiles fit into the total area to be covered.
4. Tackle the problem.
Step 1: Calculate the surface area of the sides (walls) of the pool.
- The lateral surface area (LSA) of a cuboid is calculated using the formula: \[ \text{LSA} = 2 \times ( \text{length} + \text{width} ) \times \text{height} \]
- Substituting the given values: \[ \text{LSA} = 2 \times (10 , \text{m} + 6 , \text{m}) \times 3 , \text{m} = 2 \times 16 , \text{m} \times 3 , \text{m} = 96 , \text{m}^2 \]
Step 2: Calculate the area of the base of the pool.
- The area of the base is given by: \[ \text{Area of base} = \text{length} \times \text{width} = 10 , \text{m} \times 6 , \text{m} = 60 , \text{m}^2 \]
Step 3: Find the total area to be tiled.
- Total area to be covered is the sum of the lateral surface area and the area of the base: \[ \text{Total area} = \text{LSA} + \text{Area of base} = 96 , \text{m}^2 + 60 , \text{m}^2 = 156 , \text{m}^2 \]
Step 4: Calculate the area of each tile.
- Each tile measures 20 cm x 20 cm, which in square meters is: \[ 20 , \text{cm} = 0.2 , \text{m} \quad \Rightarrow \quad \text{Area of one tile} = 0.2 , \text{m} \times 0.2 , \text{m} = 0.04 , \text{m}^2 \]
Step 5: Determine the number of tiles needed.
- To find the number of tiles required, divide the total area to be tiled by the area of one tile: \[ \text{Number of tiles} = \frac{\text{Total area}}{\text{Area of one tile}} = \frac{156 , \text{m}^2}{0.04 , \text{m}^2} = 3900 \]
Conclusion:
You will need 3900 tiles of size 20 cm x 20 cm to cover the sides and base of the pool.