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A solid right prism  has a height of 16 as shown. Also, its bases are equilateral triangles with side length 12. Points X Y Z   and  are the midpoints of edges  AC, BC, DC respectively. A part of the prism above is sliced off with a straight cut through points  X Y Z. Determine the volume of solid CXYZ ,the part that was sliced off.

 

 Jun 24, 2021
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I  believe   [ CXYZ ]    will form  an oblique  pyramid

 

Its  volume is

 

(1/3) [ XYC ]  (CD  / 2)  =

 

(1/3) [ XYC ] * 16

 

(1/6)  [ XYC ]  * 16   =

 

(1/6)   (1/2) (6)^2 sin (60°) *   16  =

 

16 * 3 sin (60°)  =

 

48 sqrt (3)  / 2   =

 

48 sqrt (3)   units^3

 

cool cool cool

 Jun 24, 2021
edited by CPhill  Jun 24, 2021

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