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 \(ABCDEFGH\)shown below is a right rectangular prism. If the volume of pyramid \(ABCH\) is 20, then what is the volume of \(ABCDEFGH\)?

tertre  Mar 17, 2018
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 #1
avatar+6949 
+3

 

The volume of a pyramid  =  (1/3) * area of base * height,   even when the height is not located above the center of the base....see https://www.mathopenref.com/pyramidvolume.html

 

(1/3) * ABC * HD  =  20 un3          so          ABC * HD  =  60 un3

 

volume of prism  =  ABCD * HD

 

ABCD  =  2 * ABC

 

volume of prism  =  2 * ABC * HD

 

volume of prism  =  2 * 60 un3


volume of prism  =  120 un3     smiley

hectictar  Mar 17, 2018
 #2
avatar+2358 
+3

Wow, great solution, hectictar! smiley

tertre  Mar 17, 2018

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