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A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying horizontally on its side. (In other words, the tank is not standing vertically on one of its flat ends.) If the radius of the cylinder is 2 meters, its length is 8 meters, and its top is 3 meters under the ground, find the total amount of work needed to pump the gasoline out of the tank. (The density of gasoline is 673 kilograms per cubic meter

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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.

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