Find the ratio of the volume of tetrahedron with that of the tetrahedron formed by the centroids of its faces. Given Volume of tetrahedron `=1/3 times` area of base triangle `times` height of vertex.

Prove that the volume of the tetrahedron and that formed by the centroids of the faces are in the ratio of 27:1.

If V be the volume of a tetrahedron and V' be the volume of another tetrahedran formed by the centroids of faces of the previous tetrahedron and V=KV', then K is equal to 9 b.12 c.27 d.81

If the edge of a regular tetrahedron is 1cm, then its volume is

The fout lines drawing from the vertices of any tetrahedron to the centroid to the centroid of the opposite faces meet in a point whose distance from each vertex is 'k' times the distance from each vertex to the opposite face, where k is

The volume of the tetrahedron with overline(a), overline(b), overline(c) as its co-terminous as is given by

Find the volume of the tetrahedron having coterminus edges represented by vectors a=j+k, b=i+k" and "c=i+j .

In the tetrahedron ABCD, A=(1,2,-3) and G(-3,4,5) is the centroid of the tetrahedron. If P is the centroid of the Delta BCD then AP=

Show that the segments joining vertices to the centroid of opposite faces of a tetrahedron are concurren Hence find the position vector of the point of concurrence.