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Calculus/volume of tetrahedron
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Question
find the volume of a tetrahedron formed by the plane x+2y+3z=6 and the coordinate planes
The volume of the tetrahedron is : V=(1/3)*A*h . Where : A is the area of the triangle base,
%26 h is the height . So, 1st step will be to find the vertices of our tetrahedron. Note that
our tetrahedron is formed by intersection between our surface x+2y+3z=6 %26 the coordinate planes.
Ok, let's find the points of intersect :
# Intersect with the z-axis : we substitute x=0%26y=0 , thus :
x+2y+3z=6 --> 0+0+3z=6 --> z=2 .
# Intersect with the y-axis : we substitute x=0%26z=0 , thus :
x+2y+3z=6 --> 0+2y+0=6 --> y=3 .
# Intersect with the x-axis : we substitute y=0%26z=0 , thus :
x+2y+3z=6 --> x+0+0=6 --> z=6 .
Our base is the triangles formed by the points : x=2,y=3,z=0 . %26 our height is z=6 . Note that
all the side triangles are right triangles !
Hence,
V=(1/3)*(1/2)*2*3*6=6 .
Alon.
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Answers by Expert:
Alon Mandes
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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
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M.A in Mathematics & Bs.c in Electronics.
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