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Find the volume of a regular hexagonal pyramid with sides 3 feet long. The lateral faces make a 35 degree angle with the base.

Guest Apr 1, 2017
 #1
avatar+87301 
+2

We need to find  the height of the pyramid.....this is given by :

 

tan (35)  =  H / [(3/2)sqrt(3)]      divide both sides by [(3/2)sqrt(3)]

 

tan (35) * [(3/2)sqrt(3)]  = H   

 

And the volume is given by :

 

(1/3) * Area of the base * height

 

And the Area of the base = 6 (1/2)*3^2* sin(60)  =  27*sin(60)

 

So....the volume is :

 

(1/3) * 27 * sin (60) * tan (35) * [(3/2)sqrt(3)]  = about 14.18 units^3

 

 

cool cool cool

CPhill  Apr 2, 2017
 #2
avatar+87301 
+1

Sorry.....my answer should have been in cubic feet........

 

 

cool cool cool

CPhill  Apr 2, 2017

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