Question

Because gasoline is less dense than water, drums containing gasoline will float in water. Suppose a 210-L steel drum is completely full of gasoline. What can the total volume of steel be used in making the drum if the gasoline-filled drum is to float in freshwater?

Short answer

The total volume of steel used to make the drum if the gasoline-filled drum is to float in freshwater is 9.9 x 10^-3m³.

Step-by-step solution

Understanding the principle of buoyancy

Buoyancy is an upward force exerted by the fluid in the upward direction that opposes the weight of a fully or partially submerged body. It is expressed in Newtons.

Identification of the given data

The volume of the gasoline in the steel drum is V_gasoline = 210L.

Determination of the total volume of steel

As the steel drum is filled with gasoline, the buoyancy force (F_B) will be equal to the sum of the weight of the steel drum (W_steel) and weight of gasoline (W_gasoline) filled inside it.

Here, m_steeland m_gasoline is the mass of the steel drum and gasoline respectively. And we know that the mass and volume ratio equals density. Thus, mass can be written as the product of volume and density.

Here, V_gasolineand V_steel are the volume of gasoline and steel drum respectively. Ρ_gasoline, ρ_steel and ρ_water are the densities of gasoline, steel and water respectively.

Rearranging,

Calculations to determine the desired result

Substitute the standard values of densities, that are, Ρ_gasoline= 680 kg/m³, ρ_steel= 7800 kg/m³and ρ_water= 1000 kg/m³, in the above formula.

Hence, the total volume of steel used to make the drum if the gasoline-filled drum is to float in freshwater is 9.9 x 10^-3m³.