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:

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

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