Oil is stored in a tank at an oil refinery.
The tank is in the shape of a cylinder.
The tank has a diameter of 20 m.
The depth of the oil in the tank is 6 m.
The density of the oil is 800 kg per m^3.
Oil tankers can hold up to 45 000 kg of oil.
How many of these oil tankers are needed to empty all the oil from the tank?
To find out how many oil tankers are needed to empty all the oil from the tank, we need to determine the volume of oil in the tank, and then divide it by the capacity of each oil tanker.
Step 1: Find the volume of the oil in the tank.
The tank is in the shape of a cylinder, so we can use the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height (or depth) of the cylinder.
Given that the diameter of the tank is 20 m, the radius (r) is half of the diameter, so r = 20/2 = 10 m.
The depth of the oil in the tank is 6 m.
Plugging in these values into the formula, we get V = π(10^2)(6).
Step 2: Calculate the volume of the oil in the tank.
Using the approximation π ≈ 3.14, we have:
V = 3.14(10^2)(6)
V = 3.14(100)(6)
V = 3.14(600)
V ≈ 1884 m^3
Step 3: Determine the number of oil tankers needed.
Since the density of the oil is 800 kg per m^3, the mass of the oil in the tank is given by:
Mass = Density × Volume
Mass = 800 × 1884
Mass ≈ 1507200 kg
Given that each oil tanker can hold up to 45,000 kg of oil, we can calculate the number of oil tankers needed by dividing the mass of oil in the tank by the capacity of each tanker:
Number of tankers = Mass of oil in the tank / Capacity of each tanker
Number of tankers ≈ 1507200 kg / 45000 kg
Step 4: Calculate the number of oil tankers needed.
Number of tankers ≈ 33.49
Since we cannot have a fraction of an oil tanker, we need to round up to the next whole number. Therefore, we would need a minimum of 34 oil tankers to empty all the oil from the tank.
To find out how many oil tankers are needed to empty all the oil from the tank, we need to calculate the volume of the oil in the tank first.
The shape of the tank is a cylinder, and we have the diameter (20 m) and the depth (6 m) of the oil.
First, we need to calculate the radius of the cylinder using the formula: radius = diameter / 2.
So, the radius would be 20 m / 2 = 10 m.
The formula to calculate the volume of a cylinder is: volume = π * radius^2 * height.
Using the given values, we have:
volume = π * (10 m)^2 * 6 m.
Now, we can calculate the volume of the oil in the tank:
volume = 3.14 * (10 m)^2 * 6 m
volume = 3.14 * 100 m^2 * 6 m
volume = 3.14 * 10,000 m^3.
Since the density of the oil is 800 kg/m^3, we can calculate the mass of the oil in the tank:
mass = volume * density
mass = 3.14 * 10,000 m^3 * 800 kg/m^3.
Finally, to find out the number of oil tankers needed, we divide the mass of the oil in the tank by the maximum capacity of each oil tanker:
number of oil tankers = mass / maximum capacity of each tanker
number of oil tankers = (3.14 * 10,000 m^3 * 800 kg/m^3) / 45,000 kg.
Performing the calculations, we can determine the number of oil tankers required to empty all the oil from the tank.
volume of the oil in the tank = pi*r^2*h = 3.14*10^2*6 = 1884 cubic meters.
mass of the oil in the tank = volume x density = 1884 m^3 x 800 kg/m^3 = 1507200 kg.
45,000 kg/tanker x # tankers = 1507200 kg. Solve for # tankers