An open concrete tank is internally 1m wide,2m long and 1.5m deep the concrete being 10cm thick.calculate:
a) the capacity of the tank in litres
b) the volume of concrete in m3
a) To find the capacity of the tank in litres, we need to use the formula:
Volume = Length x Width x Depth
Before we use this formula, we need to convert the dimensions to metres. So, the dimensions of the tank in metres are:
Width = 1m = 0.1m
Length = 2m = 0.2m
Depth = 1.5m = 0.15m
Now we can use the formula:
Volume = 0.2m x 0.1m x 0.15m
Volume = 0.003m^3
To convert this volume to litres, we multiply by 1000:
Volume in litres = 0.003m^3 x 1000
Volume in litres = 3 litres
Therefore, the capacity of the tank is 3 litres.
b) To find the volume of concrete in m3, we need to subtract the volume of the empty space inside the tank from the volume of the tank itself. The volume of the empty space is:
Volume of empty space = (Length - 2 x Thickness) x (Width - 2 x Thickness) x Depth
Volume of empty space = (2m - 2 x 0.1m) x (1m - 2 x 0.1m) x 1.5m
Volume of empty space = 1.8m x 0.8m x 1.5m
Volume of empty space = 1.44m^3
The volume of the tank itself is:
Volume of tank = Length x Width x Depth
Volume of tank = 2m x 1m x 1.5m
Volume of tank = 3m^3
Therefore, the volume of concrete in the tank is:
Volume of concrete = Volume of tank - Volume of empty space
Volume of concrete = 3m^3 - 1.44m^3
Volume of concrete = 1.56m^3
Therefore, the volume of concrete in the tank is 1.56m^3.
To calculate the capacity of the tank, we need to find the volume of the tank and convert it to liters.
a) To find the volume of the tank, we need to calculate the volume of the outer dimensions and subtract the volume of the inner dimensions.
The inner dimensions of the tank are: width = 1 m, length = 2 m, and depth = 1.5 m.
The outer dimensions of the tank can be found by adding twice the thickness of the walls to each side of the inner dimensions. Since the walls are 10 cm thick, we need to add 0.1 m to each side.
The outer dimensions of the tank are: width = 1 m + 0.1 m + 0.1 m = 1.2 m,
length = 2 m + 0.1 m + 0.1 m = 2.2 m, and
depth = 1.5 m + 0.1 m + 0.1 m = 1.7 m.
Now, we can calculate the volume of the tank:
Volume = (outer width) × (outer length) × (outer depth)
Volume = 1.2 m × 2.2 m × 1.7 m
Volume = 4.752 m³
To convert the volume from cubic meters (m³) to liters, we multiply by 1000:
Capacity = Volume × 1000
Capacity = 4.752 m³ × 1000
Capacity = 4752 liters
b) To calculate the volume of concrete in the tank, we need to find the difference between the volume of the outer dimensions and the volume of the inner dimensions.
The volume of the concrete can be calculated as:
Concrete volume = Volume (outer dimensions) - Volume (inner dimensions)
Concrete volume = 4.752 m³ - 1 m × 2 m × 1.5 m
Concrete volume = 4.752 m³ - 3 m³
Concrete volume = 1.752 m³
Therefore, the volume of concrete in the tank is 1.752 m³.