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:

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

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