Tetrahedral pyramid

Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'.

Correct answer:

S =  200.6434

Step-by-step explanation:

V=120 A=42+6030=6042 60+6030=602520+6030=602520+30=602550=285=4221=42.5  A1=A° rad=A° 180π =42.5° 1803.1415926 =0.74176=17π/72  tan A = h /(a/2)   h = a/2   tan A V = 31 a2 h V = 61 a3 tan A  a=36 V/tan(A1)=36 120/tan0.74189.2277  h=a/2 tan(A1)=9.2277/2 tan0.74184.2278 sin A1 = h : w  w=h/sin(A1)=4.2278/sin0.74186.258  S1=a w/2=9.2277 6.258/228.8733  S=a2+4 S1=9.22772+4 28.8733=200.6434



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