Wall thickness

The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm³.

Correct answer:

h =  0.6068 cm

Step-by-step explanation:

$$\begin{gathered} D=40\text{cm} \\ R=D/2=40/2=20\text{cm} \\ m=25\text{kg}\to \text{g}=25\cdot 1000\text{g}=25000\text{g} \\ \rho =8.45{\text{g/cm}}^3 \\ m=\rho V \\ V=m/\rho =25000/8.45\doteq 2958.5799{\text{cm}}^3 \\ V=V_1-V_2 \\ V=\frac{4}{3}\cdot \pi \cdot R^3-\frac{4}{3}\cdot \pi \cdot (R-h{)}^3 \\ \frac{3\cdot V}{4\pi }-R^3=-(R-h{)}^3 \\ R-h=\sqrt[3]{R^3-\frac{3\cdot V}{4\pi }} \\ h=R-\sqrt[3]{R^3-\frac{3\cdot V}{4\pi }}=R-\sqrt[3]{R^3-\frac{3\cdot \frac{500000}{169}}{4\pi }}=20-\sqrt[3]{20^3-\frac{3\cdot 2958.5799}{4\cdot 3.1416}}=0.6068\text{cm} \end{gathered}$$

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