Pyramid Height and Volume

Given is a regular quadrilateral pyramid with a square base. Side = 16 cm, S = 736 cm². Calculate h (body height) and body volume V.

Final Answer:

h =  12.6886 cm
V =  1082.7586 cm3

Step-by-step explanation:

a=16 cm S=736 cm2  S1​=a2=162=256 cm2 S2​=(S−S1​)/4=(736−256)/4=120 cm2  S2​ = a⋅ s/2 s=2⋅ S2​/a=2⋅ 120/16=15 cm  s2 = h2 + (a/2)2 h=s2−(a/2)2​=152−(16/2)2​=161​=12.6886 cm
V=31​⋅ h⋅ S1​=31​⋅ 12.6886⋅ 256=1082.7586 cm3

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