8. (15 points) The mass of a vessel completely filled with kerosene is 31 kg. If this vessel is completely filled with water, its mass will be 33 kg. Determine the mass of the empty vessel. The density of water $\rho_{W}=1000 \kappa g / \mathrm{m}^{3}$, the density of kerosene $\rho_{K}=800$ kg $/ \mathrm{m}^{3}$.
Answer: 23 kg

Solution. The mass of the vessel filled with kerosene $m_{1}=m_{c}+\rho_{K} V$,

where $m_{c}$ is the mass of the empty vessel, $V$ is the volume occupied by the kerosene. The mass of the vessel filled with water: $m_{2}=m_{c}+\rho_{b} V$. (4 points)

We get that $V=\frac{m_{2}-m_{1}}{\rho_{B}-\rho_{K}}=\frac{33-31}{1000-800}=0.01 \mathrm{~m}^{3}$.

The mass of the empty vessel: $m_{c}=m_{1}-\rho_{K} V=31-800 \cdot 0.01=23$ kg.

## Multidisciplinary Engineering Olympiad "Star"

 in natural sciences 7th grade

## Final Stage  Variant 2  Problems, answers, and evaluation criteria

$2018-2019$