SOLUTION: Let ABCDEFGH be a rectangular prism, as shown, where AB = 2, AD = 3, and AE = 5. Find the volume of pyramid ACFH.
https://latex.artofproblemsolving.com/0/a/3/0a3404805162de58ee7
Question 1074800: Let ABCDEFGH be a rectangular prism, as shown, where AB = 2, AD = 3, and AE = 5. Find the volume of pyramid ACFH.
https://latex.artofproblemsolving.com/0/a/3/0a3404805162de58ee7c86ac6b0e5d23327c0026.png Found 2 solutions by ikleyn, KMST:Answer by ikleyn(53751) (Show Source): You can put this solution on YOUR website! .
Let ABCDEFGH be a rectangular prism, as shown, where AB = 2, AD = 3, and AE = 5. Find the volume of pyramid ACFH.
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The volume of our pyramid is equal to the volume of the rectangular prism minus the volumes of three OTHER pyramids
that you can easily calculate:
= 2*3*5 - - - - - =
= 30 - - - - =
= 30 - = 30 - 20 = 10 cubic units.
Answer by KMST(5345) (Show Source): You can put this solution on YOUR website! The drawing looks (sort of) like this:
The prism has the diagonals of all its 6 faces marked.
Those diagonals split each rectangular face of the prism into two congruent right triangles,
with each of those triangles being half of a rectangular face of the prism.
Slicing along those diagonals,
they cut off 4 pyramids out of 4 corners of the prism,
to leave pyramid ACFH.
The volume of each of the pyramids cut off is of the volume of the prism.
After removing of the volume of the prism,
they are left with of the volume of the prism.
Since the volume of the prism (in cubic units) is ,
the volume left (the volume of ACFH) is .