Because gasoline is less dense than water, drums containing gasoline will float in water. Suppose a 220- L steel drum is completely full of gasoline.
What total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water?
URGENT
To determine the total volume of steel that can be used to make the drum, we need to consider the buoyant force acting on the drum. For an object to float in water, the buoyant force acting on it must be equal to or greater than its own weight.
The buoyant force is given by the formula:
Buoyant force = density of the fluid * volume of the fluid displaced * acceleration due to gravity
In this case, the fluid is fresh water, which has a density of approximately 1000 kg/m^3. We know that the drum is filled with gasoline, which is less dense than water, so the total volume of the drum must be greater than the volume of gasoline it can hold.
The volume of gasoline the drum can hold is given as 220 L. We need to convert this volume to cubic meters by dividing by 1000:
Volume of gasoline = 220 L / 1000 = 0.22 m^3
Now, assuming that the entire drum is made of steel, we can calculate the volume of steel that can be used. Let's assume the density of steel is 7850 kg/m^3:
Buoyant force = weight of the drum
density of water * volume of water displaced * acceleration due to gravity = density of steel * volume of steel * acceleration due to gravity
(1000 kg/m^3) * (0.22 m^3) * (9.8 m/s^2) = (7850 kg/m^3) * (volume of steel) * (9.8 m/s^2)
Simplifying the equation, we can solve for the volume of steel:
Volume of steel = (1000 kg/m^3 * 0.22 m^3) / (7850 kg/m^3)
Volume of steel = 0.028 m^3
Therefore, the total volume of steel that can be used in making the drum is approximately 0.028 cubic meters or 28 liters.