A garden shed is 6m long and 4m wide. A path 1.5 m wide and 10 cm deep is going to be made around the shed. What is the volume of concrete needed to lay the path?
((6+3)(4+3)-(6*4))(0.1) = 3.9 m^3
To calculate the volume of concrete needed to lay the path around the garden shed, we need to find the volume of a rectangular prism.
1. First, let's calculate the new dimensions of the shed including the path. Since the path is 1.5 m wide, we add 1.5 m to both the length and width of the shed:
New length of shed = 6 m + 1.5 m = 7.5 m
New width of shed = 4 m + 1.5 m = 5.5 m
2. Next, we need to calculate the area of the top surface of the path. Since the path extends around the shed, we can calculate the total area by subtracting the area of the shed from the area of the new dimensions:
Area of the top surface of the path = (New length of shed × New width of shed) - (Length of shed × Width of shed)
Area of the top surface of the path = (7.5 m × 5.5 m) - (6 m × 4 m)
Area of the top surface of the path = 41.25 m² - 24 m²
Area of the top surface of the path = 17.25 m²
3. Now, we can calculate the volume of the path by multiplying the area of the top surface of the path by the depth of the path:
Volume of the path = Area of the top surface of the path × Depth of the path
Remember to convert the depth of the path from centimeters to meters by dividing by 100:
Volume of the path = 17.25 m² × (10 cm ÷ 100)
Volume of the path = 17.25 m² × 0.1 m
Volume of the path = 1.725 m³
Therefore, you would need 1.725 cubic meters of concrete to lay the path.