A square pyramid has a base edge of 32 inches and an altitude of 1 foot. A square pyramid whose altitude is one-fourth of the original altitude is cut away at the apex of the original pyramid. The volume of the remaining frustum is what fractional part of the volume of the original pyramid?

 Apr 30, 2020

The "new" pyramid and the original pyramid are similar figures


The  scale  factor  of  the  "new"  pyramid  to the original pyramid  =  1/4


Let the  volume of the original pyramid  be  = V


The  volume  of the "new" pyramid  =  V *  (1/4)^3  =  V / 64


The volume  of the remaining frustum  =   V - V/64  = (63/64)V


So  the volume of the frustum  is  (63/64)  of volume of the original pyramid



cool cool cool

 Apr 30, 2020

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