Math Problem Statement
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Solution
To solve this problem, we need to find the total surface area of the walls and the floor of the pool that need to be repainted.
Step-by-step Solution:
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Dimensions of the Pool:
- Width (W): 6 m
- Length (L): 15 m
- Depth (D): 2 m
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Calculate the Floor Area: The floor of the pool is a rectangle with the length and width of the pool.
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Calculate the Wall Areas: The walls of the pool consist of two longer walls and two shorter walls.
- Longer Walls: Each longer wall has a length of 15 m and a height of 2 m.
Since there are two longer walls:
- Shorter Walls: Each shorter wall has a width of 6 m and a height of 2 m.
Since there are two shorter walls:
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Calculate the Total Surface Area to be Repainted:
The total surface area to be repainted is the sum of the floor area and the areas of all four walls.
Substituting the values:
Conclusion:
The total surface area that needs to be repainted is 174 m², which corresponds to option (B).
Would you like any further explanation or have any other questions?
Related Questions:
- What would the total surface area be if the depth of the pool were 3 m instead of 2 m?
- How would you calculate the volume of the pool?
- If the repainting cost is $5 per square meter, what would be the total cost for repainting the pool?
- How does the surface area change if the pool is circular with the same area?
- What is the perimeter of the pool?
Tip:
When working with geometry problems involving surface areas, always break down complex shapes into simpler ones, calculate each part's area, and then sum them up for the total.
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Math Problem Analysis
Mathematical Concepts
Geometry
Surface Area
Rectangular Prisms
Formulas
Floor Area = Length × Width
Wall Area = Length × Height
Total Surface Area = Floor Area + Wall Areas
Theorems
Surface area calculation for rectangular prisms
Suitable Grade Level
Grades 6-8
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