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=K V^(prime),t h e nK is equal to a. 9 b. 12 c. 27 d. 81

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=K V^(prime),t h e nK is equal to a. 9 b. 12 c. 27 d. 81

The four 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 included between the plane 3x+4y-5z-60=0 and the co-odinate planes is

The ratio of volumes of two cones is 4:5 and the ratio of the radii of their bases is 2:3. Find the ratio of their vertical heights.

If a variable plane forms a tetrahedron of constant volume 64k^3 with the co-ordinate planes, then the locus of the centroid of the tetrahedron is:

If a variable plane forms a tetrahedron of constant volume 64k^3 with the co-ordinate planes, then the locus of the centroid of the tetrahedron is:

DABC be a tetrahedron such that AD is perpendicular to the base ABC and angle ABC=30^(@) . The volume of tetrahedron is 18. if value of AB+BC+AD is minimum, then the length of AC is

Let A_(1), A_(2), A_(3), A_(4) be the areas of the triangular faces of a tetrahedron, and h_(1), h_(2), h_(3), h_(4) be the corresponding altitudes of the tetrahedron. If the volume of tetrahedron is 1//6 cubic units, then find the minimum value of (A_(1) +A_(2) + A_(3) + A_(4))(h_(1)+ h_(2)+h_(3)+h_(4)) (in cubic units).