A=The area of the horizontal cross section: A(y)=sqrt(3)/4*a^(2)
a/(h-y)=s/h --> a=(h-y)(s)/(h)
The height for a tetrahedron is:
h= sqrt(2/3)(s) --> sqrt(2/3)(7) = 5.7154
a=(h-y)(s)/(h) -->(5.7154-3)(7)/(5.7154) = 3.3257
A(y)=sqrt(3)/4*a^(2) --> sqrt(3)/4*3.3257^(2) = 4.789414
A=4.7894
Volume: V=(s^3)/(6sqrt(2)) --> (7^3)/((6sqrt(2))= 40.42297
V=40.4229
Consider a regular tetrahedron whose face is an equilateral triangle of side 7.
Find the area of the horizontal cross section A at the level z=3.
A= ?
Find the volume of the tetrahedron.
Consider a regular tetrahedron whose face is an equilateral triangle of side 7.
Find the area of the horizontal cross section A at the level z=3.
A=
Find the volume of the tetrahedron.
Consider a regular tetrahedron whose face is an equilateral triangle of side 7.
Find the area of the horizontal cross section A at the level z=3.
A= ?
Find the volume of the tetrahedron.
V=?
My work:
height = 7sin(60)= 7/2sqrt(3)
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