Frustum of a Regular Pyramid

Posted In: Mathematics

The Frustum of a regular pyramid is the result of chopping the top off a regular pyramid. It is also called truncated pyramid.

Frustum of a regular pyramid


Base and top side lengths:
$\{\table a_1,a_2,a_3,…,a_n;b_1,b_2,b_3,…,b_n$
Height: h
Slant height: m
Mi,ber of sides: n
Area of bases: S1,S2
Lateral surface area: SL
Perimeter of bases: P1,P2
Scale factor
Total surface area: S
Volume: V

  1. $b_1/a_1=b_1/a_1=b_1/a_1=…=b_n/a_n=b/a=k$
  2. $S_2/S_1=k^2$
  3. $S_L={m(P_1+P_2)}/2$
  4. $S=S_L+S_1+S_2$
  5. $V=h/3(S_1+√{S_1S_2}+S_2)$
  6. $V=hS_1/3[1+b/a+(b/a)^2]=hs_1/3[1+k+k^2]$

Post Tags: Geometry


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