Triangular pyramid

What is the volume of a regular triangular pyramid with a side 3 cm long?

Correct result:

V =  3.182 cm3

Solution:

a=3 cm  h1=a2−(a/2)2=32−(3/2)2≐2.5981 cm  h=h12−(h1/3)2=2.59812−(2.5981/3)2=6 cm≐2.4495 cm  S1=a⋅ h1/2=3⋅ 2.5981/2≐3.8971 cm2  V=13⋅ S1⋅ h=13⋅ 3.8971⋅ 2.4495=3.182 cm3

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