Euclidean Geometry #4
In the three dimensional space
. Find the volume of the triangular pyramid (irregular tretahedron) with vertex
and the points where the plane
intersects the coordinate axis.
The answer is 24.
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1 solution
Volume of triangular pyramid.
= (volume of pyramid built from plane 2x+3y+z=12 and the three axes) - (total volume of three pyramids built from the zero planes to vertex point (1,1,1)).
= [(12^3) / (6 * 2 * 3 * 1)] - [(12^2/6) * (1/(2 * 3) + 1/(3 * 1) + 1/(1 * 2))].
= 48 - (4+8+12).
= 48 - 24.
= 24