9-gon pyramid

Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.

Correct result:

V =  409.0382 cm3
S =  299.899 cm2

Solution:

ρ=7.2 cm s=10.9 cm n=9  h2+ρ2=s2  h=s2ρ2=10.927.228.1835 cm  α=2π2 n=2 3.14162 90.3491 rad  sinα=a/2:ρ  a=2 ρ sin(α)=2 7.2 sin(0.3491)4.9251 cm h2=ρ2(a/2)2=7.22(4.9251/2)26.7658 cm  S1=a h22=4.9251 6.7658216.6611 cm  S9=n S1=9 16.6611149.9495 cm2   V=13 S9 h=13 149.9495 8.1835=409.0382 cm3
S2=a h22=4.9251 10.6182216.6611 cm2 h2=h2+h22=8.18352+10.6182210.6182 cm  S=S9+n S2=149.9495+9 16.6611=299.899 cm2



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