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.

Correct result:

V =  18.0422 cm3

Solution:

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=5/2≐3.5355 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⋅ 4.3301/3=18.0422 cm3

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