Square pyramid

Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.


V =  18.042 cm3


s=5 cm A=60  cos(A)=(u/2)/s cos(A)=u/(2s) u=2 s cos(A rad)=2 s cos(A π180 )=2 5 cos(60 3.1415926180 )=5 a=u/2=5/23.5355 cm S=a2=3.53552=252=12.5 cm2 h=s sin(A rad)=s sin(A π180 )=5 sin(60 3.1415926180 )=4.33013 V=S h/3=12.5 4.3301/318.042218.042 cm3s=5 \ \text{cm} \ \\ A=60 \ ^\circ \ \\ \cos(A)=(u/2) / s \ \\ \cos(A)=u/(2s) \ \\ u=2 \cdot \ s \cdot \ \cos( A ^\circ \rightarrow\ \text{rad} )=2 \cdot \ s \cdot \ \cos( A ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=2 \cdot \ 5 \cdot \ \cos( 60 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=5 \ \\ a=u / \sqrt{ 2 }=5 / \sqrt{ 2 } \doteq 3.5355 \ \text{cm} \ \\ S=a^2=3.5355^2=\dfrac{ 25 }{ 2 }=12.5 \ \text{cm}^2 \ \\ h=s \cdot \ \sin( A ^\circ \rightarrow\ \text{rad} )=s \cdot \ \sin( A ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=5 \cdot \ \sin( 60 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=4.33013 \ \\ V=S \cdot \ h / 3=12.5 \cdot \ 4.3301 / 3 \doteq 18.0422 \doteq 18.042 \ \text{cm}^3

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