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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.

 

 Jan 18, 2021
 #1
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A solid right prism has a height of 16 as shown. Also, its bases are equilateral triangles with a side length of 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.

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A solid CXYZ is a pyramid with an equilateral triangle as its base.

 

Solid height       h = 8

 

Base area          A = 1/4 * √3 * a2              a = 6              

 

Solid volume      V = 1/3 * A * h         

 

 

 Jan 19, 2021
edited by jugoslav  Jan 19, 2021
edited by jugoslav  Jan 19, 2021

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