Wood floats

A wooden cylinder with a diameter of 20 cm and a length of 1 m is immersed in water. The specific weight of wood is 700kg/m³. For example, calculate the height of the wood that is above the water. The role was assigned to me as a high school freshman math entrance exam 52 years ago.

Correct answer:

x =  0.3 m

Step-by-step explanation:

$$\begin{gathered} D=20\text{cm}\to \text{m}=20:100\text{m}=0.2\text{m} \\ h=1\text{m} \\ {\rho }_1=700{\text{kg/m}}^3 \\ {\rho }_2=1000{\text{kg/m}}^3 \\ {F}_1=F_2 \\ m=\rho V \\ F=mg \\ g\cdot {\rho }_1\cdot V_1=g\cdot {\rho }_2\cdot V_2 \\ {\rho }_1\cdot V_1={\rho }_2\cdot V_2 \\ {\rho }_1\cdot S_1\cdot h={\rho }_2\cdot S_1\cdot (h-x) \\ {\rho }_1\cdot h={\rho }_2\cdot (h-x) \\ 700\cdot 1=1000\cdot (1-x) \\ 1000x=300 \\ x=\frac{300}{1000}=0.3 \\ x=\frac{3}{10}=0.3=0.3\text{m} \end{gathered}$$

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