Float boya

A spherical float with a diameter of 0.5 m marks the location of a fishing boat's anchor. It floats in salt water. Find the depth to which the float sinks if the material it is made of has a density of 8 kg/m³ and salt water has a density of 1,027 kg/m³.

Final Answer:

h =  0.0446 m

Step-by-step explanation:

$$\begin{gathered} R=0.5\text{m} \\ {\rho }_1=8{\text{kg/m}}^3 \\ {\rho }_2=1027{\text{kg/m}}^3 \\ m=\rho V \\ {m}_1=m_2 \\ {\rho }_1\cdot 4/3\cdot \pi R^3={\rho }_2/3\cdot \pi h^2(4R-h) \\ 8\cdot 4/3\cdot \pi 0.5^3=1027/3\cdot \pi h^2(4\cdot 0.5-h) \\ 4.18879=(2150.94-1075.47h)h^2 \\ {h}_1=-0.0436557\doteq -0.0437 \\ {h}_2=0.0446304\doteq 0.0446 \\ {h}_3=1.99903\doteq 1.999 \\ 0<h<2R \\ h=0.0446304=0.0446\text{m} \end{gathered}$$

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