Determine 3784

The teacher brought to class two wooden models of cones, which were made of the same type of wood. The first model weighed 800g. The other had twice the base radius but half the height. Determine the mass of the second cone in grams.

Correct answer:

m₂ =  1600 g

Step-by-step explanation:

$$\begin{gathered} m_1=800 \\ {r}_2=2r_1 \\ {h}_2=h_1/2 \\ k=\pi /3H \\ {m}_1=k{r}_1^2{h}_1 \\ {m}_2=k{r}_2^2{h}_2=k4r_1^2{h}_1/2 \\ {m}_2=2k{r}_1^2{h}_1=2m_1 \\ {m}_2=2\cdot m_1=2\cdot 800=1600\text{g} \end{gathered}$$

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