Cheops pyramid

The Pyramid of Cheops is a pyramid with a square base with a side of 233 m and a height of 146.6 m. It is made from limestone with a density of 2.7 g/cm³. Calculate the amount of stone in tons. How many trains with 30 twenty-ton wagons carry the stone?

Final Answer:

m =  7162891 t
n =  11938.1511

Step-by-step explanation:

$$\begin{gathered} a=233\text{m} \\ h=146.6\text{m} \\ \rho =2.7{\text{g/cm}}^3\to {\text{kg/m}}^3=2.7\cdot 1000{\text{kg/m}}^3=2700{\text{kg/m}}^3 \\ {S}_1=a^2=233^2=54289{\text{m}}^2 \\ V=\frac{1}{3}\cdot S_1\cdot h=\frac{1}{3}\cdot 54289\cdot 146.6\doteq 2652922.4667{\text{m}}^3 \\ {m}_1=[\rho \cdot V]=[2700\cdot 2652922.4667]=7162890660\text{kg} \\ m=m_1\to \text{t}=m_1:1000\text{t}=7162890660:1000\text{t}=7162891\text{t}=7162891\text{t} \end{gathered}$$

$$\begin{gathered} m_2=30\cdot 20=600\text{t} \\ n=m/m_2=7162890.66/600=11938.1511 \end{gathered}$$

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