Brass ball

What is the weight of a hollow brass ball, the outer diameter of which is 16 cm and the wall thickness is 2 cm, while the density of brass is ϱ = 8.5 g

Correct answer:

m =  10.539 kg

Step-by-step explanation:

$$\begin{gathered} D=16\text{cm} \\ R=D/2=16/2=8\text{cm} \\ h=2\text{cm} \\ r=R-h=8-2=6\text{cm} \\ \rho =8.5{\text{g/cm}}^3 \\ {V}_1=\frac{4}{3}\cdot \pi \cdot R^3=\frac{4}{3}\cdot 3.1416\cdot 8^3\doteq 2144.6606{\text{cm}}^3 \\ {V}_2=\frac{4}{3}\cdot \pi \cdot r^3=\frac{4}{3}\cdot 3.1416\cdot 6^3\doteq 904.7787{\text{cm}}^3 \\ V=V_1-V_2=2144.6606-904.7787\doteq 1239.8819{\text{cm}}^3 \\ {m}_1=\rho \cdot V=8.5\cdot 1239.8819\doteq 10538.9962\text{g} \\ m=m_1\to \text{kg}=m_1:1000\text{kg}=10538.9962:1000\text{kg}=10.539\text{kg}=10.539\text{kg} \end{gathered}$$

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