A 2.50-kg steel gasoline can holds 20.0 L of gasoline when full. What is the average density of the full gas can, taking into account the volume occupied by steel as well as by gasoline?

A 2.50-kg steel gasoline can holding 20.0 L of gasoline has an average density of 0.875 kg/L.

A 2.50-kg steel gasoline can holds 20.0 L (V) of gasoline when full.

Since the density of gasoline is 0.7489 kg/L, the mass (m(g)) of 20.0 L of gasoline is:

The total mass (m) will be the sum of the mass of the steel can (m(s)) and the mass of the gasoline (m(g)).

The average density (ρ) will be the ratio of the total mass (m) to the total volume (V).

A 2.50-kg steel gasoline can holding 20.0 L of gasoline has an average density of 0.875 kg/L.

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The average density of the full gas can is , assuming the standard density of gasoline to be .

Explanation:

Given the mass of the can () is 2.5 Kg and the volume (V) occupied by gasoline is 20 L. Assuming the standard density of gasoline () to be 748.9 , if '' be the mass of the gasoline occupied in the entire can, then

If '' be the average density of the full gas can, then

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west