# Roof 8

How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.

Result

V =  26095 l

#### Solution:

$a=3.6 \cdot \ 10=36 \ \\ h=2.5 \cdot \ 10=25 \ \\ S_{1}=\sqrt{ 3 }/4 \cdot \ a^2=\sqrt{ 3 }/4 \cdot \ 36^2 \doteq 324 \ \sqrt{ 3 } \doteq 561.1845 \ \\ S=6 \cdot \ S_{1}=6 \cdot \ 561.1845 \doteq 1944 \ \sqrt{ 3 } \doteq 3367.1068 \ \\ V_{1}=S \cdot \ h/3=3367.1068 \cdot \ 25/3 \doteq 28059.2231 \ \\ V=(1-7/100) \cdot \ V_{1}=(1-7/100) \cdot \ 28059.2231 \doteq 26095.0775 \doteq 26095 \ \text{l}$

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