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**+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

CPhill
Apr 2, 2017