A cylinder water tank, lying horizontally, 1.2 m. in diameter and 3 m long is filled to a depth of 0.90 m. How many liters of water does it contain?
Look at the cross-section. The area of the unfilled pipe is a segment with area
1/2 r^2 (θ-sinθ)
where cos(θ/2) = .3/1.2 = .25
so, θ = 1.31, sinθ = 0.968
That makes the volume of water
(0.36π - 0.18(1.31-0.968))*3 = 3.208 m^3
To find the volume of water in the tank, we can use the formula for the volume of a cylinder:
Volume = π × r^2 × h
Given:
Diameter of the tank (d) = 1.2 m
Radius of the tank (r) = d/2 = 1.2/2 = 0.6 m
Length of the tank (h) = 3 m
Depth of water (d) = 0.90 m
Substituting the values into the formula:
Volume = π × (0.6)^2 × 0.90
Calculating the values:
Volume = 3.14 × 0.36 × 0.90
Volume = 1.0184 m^3
Now, we need to convert the volume from cubic meters to liters. Since 1 cubic meter is equal to 1000 liters:
Volume (in liters) = 1.0184 × 1000
Volume (in liters) ≈ 1018.4 liters
Therefore, the water tank contains approximately 1018.4 liters of water.
To find the volume of water in the cylinder, we need to calculate the volume of a cylindrical shape.
The formula for the volume of a cylinder is:
V = πr^2h
Where:
V is the volume,
π is a constant (approximately 3.14159),
r is the radius of the cylinder, and
h is the height of the cylinder.
Given:
Diameter = 1.2 m
Radius (r) = Diameter/2 = 1.2/2 = 0.6 m
Height (h) = 3 m
Depth = 0.90 m
To find the volume of water, we need to find the height of water in the cylinder. Since the tank is lying horizontally, the depth of water is equivalent to the height of water.
The volume of water can be calculated as follows:
V = πr^2h
= 3.14159 x (0.6^2) x 0.9
= 1.69317 cubic meters
1 cubic meter is equal to 1000 liters. So, to convert cubic meters to liters, we multiply by 1000.
Volume of water in liters = 1.69317 x 1000
= 1693.17 liters
Therefore, the water tank contains approximately 1693.17 liters of water.