Heptagonal pyramid

A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the density of the wood is 10 grams/cm3.

Correct result:

m =  17.3972 kg

Solution:

s1=18 cm s2=14 cm h=30 cm   n=7  S1=14 n s1 cotg(π/n)=14 7 18 cotg(3.1416/7)65.4104 cm2 S2=14 n s2 cotg(π/n)=14 7 14 cotg(3.1416/7)50.8748 cm2  V=13 h (S1+S2+S1 S2)=13 30 (65.4104+50.8748+65.4104 50.8748)1739.7177 cm3   ρ=10 g/cm3  m1=ρ V=10 1739.717717397.177 g  m=m1 kg=m1/1000  kg=17397.177/1000  kg=17.397 kg=17.3972 kg



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