A cylindrical tank with flat ends has a diameter of two meters and is 5meters long. It is filled with fuel to a depth of one and one-half meters. Find the volume of the fuel in the tank in liters.
plsss help!!
To find the volume of the fuel in the tank, we will first calculate the volume of the entire cylindrical tank and then subtract the volume of the empty space above the fuel.
Step 1: Calculate the volume of the cylindrical tank
The formula for the volume of a cylinder is given by V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given:
Diameter of the tank = 2 meters
Radius, r = diameter / 2 = 2 / 2 = 1 meter
Height of the tank, h = 5 meters
Using the formula, the volume of the cylindrical tank (including the empty space above the fuel) is:
V_tank = π * (1)^2 * 5
V_tank = π * 1 * 1 * 5
V_tank = 5π cubic meters
Step 2: Calculate the volume of the empty space above the fuel
The empty space above the fuel is a cylinder with the same diameter (2 meters) and a height of (5 - 1.5) = 3.5 meters, since the fuel depth is given as one and one-half meters.
Using the formula, the volume of the empty space is:
V_empty = π * (1)^2 * 3.5
V_empty = π * 1 * 1 * 3.5
V_empty = 3.5π cubic meters
Step 3: Calculate the volume of the fuel
The volume of the fuel is obtained by subtracting the volume of the empty space above the fuel from the volume of the entire cylindrical tank.
V_fuel = V_tank - V_empty
V_fuel = 5π - 3.5π
V_fuel = 1.5π cubic meters
Step 4: Convert the volume to liters
1 cubic meter is equal to 1000 liters.
So, the volume of the fuel in liters is:
V_fuel_liters = V_fuel * 1000
V_fuel_liters = 1.5π * 1000
V_fuel_liters = 1500π liters
Therefore, the volume of the fuel in the tank is 1500π liters.
To find the volume of the fuel in the tank, we need to calculate the volume of the cylinder and then subtract the volume of the empty space above the fuel level.
First, let's find the volume of the cylinder. The formula for the volume of a cylinder is:
V_cylinder = π * r^2 * h
Given:
Diameter of the tank (d) = 2 meters
Radius of the tank (r) = d/2 = 2/2 = 1 meter
Length of the tank (h) = 5 meters
Using these values, we can calculate the volume of the cylinder:
V_cylinder = π * (1)^2 * 5
V_cylinder = 5π cubic meters (since the radius and length are in meters)
Now, we need to find the volume of the empty space above the fuel level. This is essentially a smaller cylinder with the same radius but a different height. The height of this empty space can be found by subtracting the depth of the fuel from the total height of the tank:
Empty space height = Total height - Fuel depth
Empty space height = 5 - 1.5
Empty space height = 3.5 meters
Now, we can calculate the volume of the empty space using the formula for the volume of a cylinder:
V_empty_space = π * (1)^2 * 3.5
V_empty_space = 3.5π cubic meters
Finally, to find the volume of the fuel, we subtract the volume of the empty space from the volume of the cylinder:
V_fuel = V_cylinder - V_empty_space
V_fuel = 5π - 3.5π
V_fuel = 1.5π cubic meters
However, since we want the volume in liters, we need to convert cubic meters to liters. Since 1 cubic meter is equal to 1000 liters, the volume of the fuel in liters is:
V_fuel_liters = V_fuel * 1000
V_fuel_liters = (1.5π) * 1000
So, the volume of the fuel in the tank is approximately 4712.39π liters.
V = πr^2h
With the above, r = 1m and h = 1.5m
1 m^3 = 1000 liters.
I'll let you do the calculations.