An open concrete tank is internally 1m wide,2m long and 1.5m deep ,the concrete being 10cm thick .calculate the capacity of the tank in litres and the volume of concrete used in metre cube
The internal dimensions of the tank are:
Length L = 2m
Width W = 1m
Depth D = 1.5m
The thickness of the concrete is 10cm = 0.1m
To calculate the capacity of the tank in litres, we need to calculate the volume of the tank. The formula for the volume of a rectangular tank is:
Volume = Length × Width × Depth
Therefore, the volume of the tank is:
Volume = 2m × 1m × 1.5m
Volume = 3m³
To calculate the capacity of the tank in litres, we need to convert the volume from cubic metres to litres. There are 1,000 litres in a cubic metre, so:
Capacity = Volume × 1,000
Capacity = 3m³ × 1,000
Capacity = 3,000 litres
To calculate the volume of concrete used in the tank, we need to subtract the volume of the tank from the volume of the tank with the concrete walls. The dimensions of the tank with the concrete walls are:
Length L = 2.2m (2m + 2 × 0.1m)
Width W = 1.2m (1m + 2 × 0.1m)
Depth D = 1.6m (1.5m + 2 × 0.1m)
The volume of the tank with the concrete walls is:
Volume = Length × Width × Depth
Volume = 2.2m × 1.2m × 1.6m
Volume = 4.224m³
The volume of the tank is:
Volume = Length × Width × Depth
Volume = 2m × 1m × 1.5m
Volume = 3m³
Therefore, the volume of concrete used in the tank is:
Volume of concrete = Volume of tank with walls - Volume of tank
Volume of concrete = 4.224m³ - 3m³
Volume of concrete = 1.224m³
Therefore, the capacity of the tank is 3,000 litres and the volume of concrete used in the tank is 1.224m³.
To calculate the capacity of the tank in liters, we need to find the volume of the tank excluding the thickness of the concrete.
Step 1: Find the internal volume of the tank:
Volume of the tank = width x length x depth
= 1m x 2m x 1.5m
= 3 cubic meters
Step 2: Find the thickness of the concrete:
Thickness = 10cm = 0.1m
Step 3: Calculate the capacity of the tank:
Capacity = Volume of the tank - Volume of the concrete
= 3 cubic meters - (1m x 2m x 0.1m)
= 3 cubic meters - 0.2 cubic meters
= 2.8 cubic meters
Step 4: Convert the capacity to liters:
1 cubic meter = 1000 liters
Capacity = 2.8 cubic meters x 1000 liters
= 2800 liters
Therefore, the capacity of the tank is 2800 liters.
Now, let's calculate the volume of concrete used in cubic meters:
Step 1: Find the external dimensions of the tank:
External width = Internal width + 2 x thickness of the concrete
= 1m + 2 x 0.1m
= 1m + 0.2m
= 1.2m
External length = Internal length + 2 x thickness of the concrete
= 2m + 2 x 0.1m
= 2m + 0.2m
= 2.2m
External depth = Internal depth + thickness of the concrete
= 1.5m + 0.1m
= 1.6m
Step 2: Find the volume of the tank including the concrete:
Volume of the tank = external width x external length x external depth
= 1.2m x 2.2m x 1.6m
= 4.224 cubic meters
Step 3: Calculate the volume of the concrete used:
Volume of concrete = Volume of the tank - Volume of the internal tank
= 4.224 cubic meters - 3 cubic meters
= 1.224 cubic meters
Therefore, the volume of concrete used in the tank is 1.224 cubic meters.