Quadrilateral 81385

A regular quadrilateral pyramid with base edge length a = 15cm and height v = 21cm is given. We draw two planes parallel to the base, dividing the height of the pyramid into three equal parts. Calculate the ratio of the volumes of the 3 bodies created.

Correct answer:

r = 1:7:19

Step-by-step explanation:

a3=15 cm v3=21 cm  V3=31 a32 v3=31 152 21=1575 cm3  v1=31 v3=31 21=31 21=321=7 cm a1=v3v1 a3=217 15=217 15=21105=5 cm V1=31 a12 v1=31 52 7=3175=583158.3333 cm3  v2=32 v3=32 21=32 21=342=14 cm a2=v3v2 a3=2114 15=2114 15=21210=10 cm V2=31 a22 v2=31 102 14=31400=46632466.6667 cm3  A=V1=58.3333=3175=583158.3333 cm3 B=V2V1=466.666758.3333=31225=40831408.3333 cm3 C=V3V2=1575466.6667=33325=1108311108.3333 cm3  r1=A:B=58.3333:408.3333=710.1429=1:7 r2=B:C=408.3333:1108.3333=1970.3684=7:19  r=1:7:19

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