Mathematics Notes - Solid Geometry Problems and Solutions

How many cubic yards of material are needed for the foundation of a barn 40 ft by 80 ft, if the foundation is 2 ft thick and 12 ft high?

$a barn 40 ft by 80 ft, if the foundation is 2 ft thick and 12 ft high$

$Vol_{p}= L ~ x ~ W ~ H$

$Vol = Vol_{outside} - Vol_{inside}$

$Vol_{outside}= 40x80x12 $

$Vol_{outside}= 38400 ~ ft^3 $

To calculate the volume of the inside rectangular parallelepiped, solve first the dimensions.

The length is $80-4 = 76 ~ft$ and the width is $40-4 = 36 ~ft$

$Vol_{inside}= 36x76x12 $

$Vol_{inside}= 32832 ~ft^3 $

$Vol = 38400 - 32832$

$Vol = 5568 ~ft^3$

$Vol = \frac{5568}{27} ~yd^3$, $1 yd^3 = 27 ft^3$

$Vol = 206.22 ~yd^3$