Math Problem Statement
Solve it
Solution
Let's break down the problem:
Given:
- The garden is 100 m long and 50 m wide.
- There is a road of 3 m wide around the garden.
- The cost of paving the road is Rs. 250 per square meter.
To Find:
The total cost of paving the road.
Approach:
-
Area of the garden (without the road):
- Length = 100 m
- Width = 50 m
-
Area of the garden including the road:
- Since the road is around the garden, the total dimensions increase by 3 m on each side.
- New Length =
- New Width =
-
Area of the road: The area of the road is the difference between the area of the garden with the road and the area of the garden without the road:
-
Cost of paving the road: The cost is given as Rs. 250 per square meter.
Answer:
The cost of paving the road is Rs. 234,000.
Would you like more details, or do you have any further questions?
Here are 5 related questions for practice:
- If the cost per square meter increased to Rs. 300, what would be the new total cost?
- How much area would the road cover if the garden was square, with a side length of 60 meters?
- What would be the cost if the road was only 2 meters wide instead of 3 meters?
- How would the area of the road change if the garden was 150 m long and 70 m wide?
- How much would it cost to pave a circular road with a radius of 5 meters around a circular garden?
Tip: When calculating areas, always account for the increase in dimensions on both sides when something surrounds a given area.
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Math Problem Analysis
Mathematical Concepts
Area Calculation
Cost Calculation
Geometry
Formulas
Area = Length × Width
Area of the garden with road = (Length + 2 × Road Width) × (Width + 2 × Road Width)
Cost = Area of road × Cost per square meter
Theorems
-
Suitable Grade Level
Grades 6-8
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