Hollow sphere

Calculate the weight of a hollow stříbrné sphere (density 10.5 g/cm³) if the vnitřní diameter is 15 cm and wall thickness is 1 mm.

Correct answer:

m =  752.1 g

Step-by-step explanation:

$$\begin{gathered} \rho =10.5{\text{g/cm}}^3 \\ D=15\text{ mm } \\ h=1\text{ mm}\to \text{ cm}=1\mathrm{/}10\text{ cm}=0.1\text{ cm } \\ {r}_1=D\mathrm{/}2+h=15\mathrm{/}2+0.1={\displaystyle \frac{38}{5}}=7.6\text{ cm } \\ {r}_2=D\mathrm{/}2=15\mathrm{/}2={\displaystyle \frac{15}{2}}=7.5\text{ cm } \\ {V}_1={\displaystyle \frac{4}{3}}\cdot \pi \cdot r_1^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 7.6^3\doteq 1838.7784{\text{cm}}^3 \\ {V}_2={\displaystyle \frac{4}{3}}\cdot \pi \cdot r_2^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 7.5^3\doteq 1767.1459{\text{cm}}^3 \\ V=V_1-V_2=1838.7784-1767.1459\doteq 71.6325{\text{cm}}^3 \\ m=\rho \cdot V=10.5\cdot 71.6325=752.1\text{ g} \end{gathered}$$

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