# 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 made from limestone with a density of 2.7 g/cm3. Calculate the amount of stone in tons. How many trains with 30 twenty tons wagons carry the stone?

Result

m =  7162891 t
n =  11938.152

#### Solution:

$a=233 \ \text{m} \ \\ h=146.6 \ \text{m} \ \\ \ \\ ρ=2.7 \ g/cm^3 \rightarrow kg/m^3=2.7 \cdot \ 1000 \ kg/m^3=2700 \ kg/m^3 \ \\ \ \\ S_{1}=a^2=233^2=54289 \ \text{m}^2 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{1} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 54289 \cdot \ 146.6 \doteq 2652922.4667 \ \text{m}^3 \ \\ \ \\ m_{1}=ρ \cdot \ V=2700 \cdot \ 2652922.4667=7162890660.01 \ \text{kg} \ \\ \ \\ m=m_{1} \rightarrow t=m_{1} / 1000 \ t=7162890660.01 / 1000 \ t=7162890.66001 \ t=7162891 \ \text{t}=7.162891\cdot 10^{ 6 } \ \text{t}$
$m_{2}=30 \cdot \ 20=600 \ \text{t} \ \\ \ \\ n=m/m_{2}=7162890.66/600 \doteq 11938.1517 \doteq 11938.152$

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