Top of the tower

The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joints, overlap and waste?

Correct result:

S =  7.8986 m2

Solution:

a=1.2 m h=1.6 m n=6  h12+(a/2)2=a2  h1=a2a2/4=1.221.22/41.0392 m  h2=h2+h12=1.62+1.039221.9079 m S1=n a h22=6 1.2 1.907926.8684 m2 q=15%=1+15100=1.15  S=q S1=1.15 6.8684=7.8986 m2



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Showing 2 comments:
#
Mathematican
We need to find the apothem (a) of the base first, so then you can find the height of a triangle of the face since you don't have this, just the height of the pyramid.

0.62 + a2 = 1.22 then this a is the apothem, and you can use to find the height of "triangle a face". So h2 2 = 1.62 + a2. And now you do what it is written with these new values.

#
Mathematican
Thank Luiza. We just corrected this pyramid problem. So h is the height of the whole pyramid, h2 is wall height and h1 is now the height of the base triangles (hexagon is composed of six equilateral triangles).

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