Cylindrical 16713

Twenty identical steel balls were dropped into a cylindrical container of water standing on a horizontal surface to submerge them below the surface. At the same time, the water level rose by 4 mm. Determine the radius of one sphere if the diameter of the cylindrical container is 4.7 cm.

Correct answer:

r =  4.3592 mm

Step-by-step explanation:

$$\begin{gathered} n=20 \\ h=4\text{mm} \\ D=4.7\text{cm}\to \text{mm}=4.7\cdot 10\text{mm}=47\text{mm} \\ R=D/2=47/2=\frac{47}{2}=23.5\text{mm} \\ V=\pi \cdot R^2\cdot h=3.1416\cdot 23.5^2\cdot 4\doteq 6939.7782{\text{mm}}^3 \\ {V}_1=V/n=6939.7782/20\doteq 346.9889{\text{mm}}^3 \\ {V}_1=\frac{4}{3}\cdot \pi r^3 \\ r=\sqrt[3]{\frac{V_1\cdot 3}{4\pi }}=\sqrt[3]{\frac{346.9889\cdot 3}{4\cdot 3.1416}}=4.3592\text{mm} \end{gathered}$$

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