Answer: To find the total amount of work needed to pump the gasoline out of the tank, we'll need to calculate the volume of gasoline in the tank and then find the work done against gravity to lift it out.
Step 1: Calculate the volume of gasoline in the tank.
The tank is in the shape of a cylinder, and the formula to calculate the volume of a cylinder is:
Volume = π * r^2 * h
where:
π is the mathematical constant pi (approximately 3.14159)
r is the radius of the cylinder
h is the height (length) of the cylinder
Given values:
Radius (r) = 2 meters
Height (h) = 8 meters
Volume = π * (2)^2 * 8
Volume = π * 4 * 8
Volume = 32π cubic meters
Step 2: Find the mass of gasoline in the tank.
The density of gasoline is given as 673 kilograms per cubic meter.
Mass = Density * Volume
Mass = 673 kg/m^3 * 32π m^3
Step 3: Calculate the work done against gravity to lift the gasoline out of the tank.
The work done against gravity is given by the formula:
Work = Force * Distance
The force required to lift the gasoline is equal to its weight, which can be calculated using:
Force = Mass * Gravity
where:
Gravity is the acceleration due to gravity (approximately 9.81 m/s^2).
Force = 673 kg/m^3 * 32π m^3 * 9.81 m/s^2
Now, we need to calculate the distance over which the gasoline needs to be lifted. The top of the tank is 3 meters under the ground, so the distance is:
Distance = height of the tank = 8 meters
Work = Force * Distance
Work = (673 kg/m^3 * 32π m^3 * 9.81 m/s^2) * 8 meters
Step 4: Calculate the total amount of work in joules.
To get the total work in joules, we simply multiply the value obtained in the previous step by the gravitational constant (9.81 m/s^2):
Total work = (673 kg/m^3 * 32π m^3 * 9.81 m/s^2) * 8 meters * 9.81 m/s^2
Now, let's compute the result:
Total work ≈ 5,057,212 joules
So, the total amount of work needed to pump the gasoline out of the tank is approximately 5,057,212 joules.