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

Volume of tetrahedron and parallelepiped

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.

The lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.

The lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent.

The volume of two sphere are in the ratio 8:27. The ratio of their surface area is :

If the volume of the tetrahedron formed by the coterminus edges bara,barb and barc is 4, then the volume of the parallelopiped formed by the coterminous edges baraxxbarb,barbxxbarc and barcxxbara is