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ABCDEFGH shown below is a cube with volume 240. Find the volume of pyramid ABCH.

 

 Dec 1, 2020
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ABCH  will  result in an oblique pyramid...its volume will be  (1/6)  that of the  cube =  40 

 

Proof  ....

 

Volume of  cube =  s^3   where  s is a side  length of the  cube

 

Volume of the pyramid  =

 

(1/3)   area of base *   height

 

area of base  =  (1/2) s^2

height =  s

 

So....

 

Volume of the  pyramid =  

 

(1/3) (1/2)s^2 * s   =

 

(1/6)s^3  =  (1/6) (240)  =  40  ( units^3 )

 

cool cool cool

 Dec 1, 2020

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