Quadrangular pyramid

Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.

Correct result:

a =  10 cm
S =  708.2763 cm2

Solution:

h=30 cm V=1000 cm3  V=13hS1  S1=3⋅ V/h=3⋅ 1000/30=100 cm2  S1=a2  a=S1=100=10 cm
h2=h2+(a/2)2=302+(10/2)2=5 37 cm≐30.4138 cm S2=a⋅ h2/2=10⋅ 30.4138/2=25 37 cm2≐152.0691 cm2  S=S1+4⋅ S2=100+4⋅ 152.0691=708.2763 cm2

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