Pyramid model

Peter brought back from his vacation in Egypt a model pyramid in the shape of a regular quadrilateral pyramid. He measured that its base edge has a length of 7 cm and the lateral edge has a length of 10 cm. The model has a mass of 1 kg and is made of an unknown metal. What metal is the model made of? The table of densities will help you.

Metal	Density in g/cm3
Lead	11.34
Silver	10.5
Zinc	7.06
Iron	7.60

Final Answer:

x = Zn

Step-by-step explanation:

$$\begin{gathered} m=1\text{kg}\to \text{g}=1\cdot 1000\text{g}=1000\text{g} \\ a=7\text{cm} \\ S=a^2=7^2=49{\text{cm}}^2 \\ s=10\text{cm} \\ u=\sqrt{2}\cdot a=\sqrt{2}\cdot 7=7\sqrt{2}\text{cm}\doteq 9.8995\text{cm} \\ h=\sqrt{s^2-(u/2{)}^2}=\sqrt{10^2-(9.8995/2{)}^2}\doteq 8.6891\text{cm} \\ V=\frac{1}{3}\cdot S\cdot h=\frac{1}{3}\cdot 49\cdot 8.6891\doteq 141.9215{\text{cm}}^3 \\ \rho =m/V=1000/141.9215\doteq 7.0461{\text{g/cm}}^3 \\ x=Zn \end{gathered}$$

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