# Bricks pyramid

How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?

Result

n =  107122667

#### Solution:

$278 \ m = 2780 \ dm = 2^2 \times 5 \times 139 \ dm \ \\ 272 \ m = 2720 \ dm = 2^5 \times 5 \times 17 \ dm \ \\ \ \\ a = 272 \ m \ \\ h = 278 \ m \ \\ \ \\ x = 50 \ cm = 50 / 100 \ m = 0.5 \ m \ \\ y = 32 \ cm = 32 / 100 \ m = 0.32 \ m \ \\ z = 40 \ cm = 40 / 100 \ m = 0.4 \ m \ \\ \ \\ V_{ 0 } = x \cdot \ y \cdot \ z = 0.5 \cdot \ 0.32 \cdot \ 0.4 = \dfrac{ 8 }{ 125 } = 0.064 \ m^3 \ \\ V = \dfrac{ 1 }{ 3 } \cdot \ a^2 \cdot \ h = \dfrac{ 1 }{ 3 } \cdot \ 272^2 \cdot \ 278 \doteq 6855850.6667 \ m^3 \ \\ \ \\ n = V/V_{ 0 } = 6855850.6667/0.064 \doteq 107122666.667 = 107122667 = 1.071227\cdot 10^{ 8 }$

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