A solid body floats in a liquid at a temperature `t = 50^@ C` being completely submerged in it. What percentage of the volume of the body is submerged in the liquid after it is cooled to `t_0 = 0^@ C`, if the coefficient of cubic expansion for the solid is `gamma_s = 0.3 xx 10^-5 .^@ C^-1` and of the liquid `gamma_l = 8 xx 10^-5 .^@ C^-1`.

Explanation

To solve the problem, we need to determine the percentage of the volume of a solid body that is submerged in a liquid after the temperature is lowered from \( t = 50^\circ C \) to \( t_0 = 0^\circ C \). We will use the coefficients of cubic expansion for both the solid and the liquid.

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
At \( t = 50^\circ C \), the solid body is completely submerged in the liquid. The densities of the solid and liquid at this temperature are equal, which can be expressed as:
\[
\rho_{s, 50} = \rho_{l, 50}
...