Question

An architect is designing a pyramid-shaped building that is cut off in a plane parallel to its base.
Dimensions of the building: $64m\times 64m\times 36m$
Dimensions of the cut off section: $16m\times 16m\times 12m$

Determine the volume of the building.

• A. $64,512m^3$
• B. $1024m^3$
• C. $64,000m^3$
• D. $65,536m^3$

Answer 1

The correct option is A $64,512m^3$

Volume of the building = Volume of the entire pyramid Volume of − the cut off section
Volume of the entire pyramid = 1 Base area Height

$\frac{1}{3}\times 64\times 64\times 48=65,536m^3$

Volume of the cut off section = 1 Base area Height

$\frac{1}{3}\times 16\times 16\times 12=1024m^3$

Volume of the building
$=65,536-1024=64,512m^3$