One barrel is filled with water and the other with kerosene, which barrel is larger

One barrel is filled with water and the other with kerosene, which barrel is larger in diameter if it is known that the level and mass of both liquids are the same?

Given:

m1 = m2 = m – the mass of barrels filled with water and kerosene is the same;

h1 = h2 = h – the level of the barrels filled with water and kerosene is the same;

ro1 = 1000 kg / m3 – water density;

ro2 = 800 kg / m3 – density of kerosene.

It is required to determine which of the drums has the largest diameter.

It is known from the problem statement that the mass of the barrels is the same. Then:

m1 = m2;

ro1 * V1 = ro2 * V2, where V1 and V2 are barrel volumes;

ro1 * S1 * h = ro2 * S2 * h, where S1 and S2 are the bottom area of ​​the barrels;

ro1 * S1 = ro2 * S2;

ro1 * pi * d1 ^ 2/4 = ro2 * pi * d2 ^ 2/4;

ro1 * d1 ^ 2 = ro2 * d2 ^ 2;

d1 = (ro2 / ro1) ^ 0.5 * d ^ 2;

d1 = (800/1000) ^ 0.5 * d ^ 2;

d1 = 0.9 * d ^ 2.

From the solution obtained, it can be seen that the diameter of the kerosene barrel is larger.

Answer: the kerosene barrel has a larger diameter.