If V be the volume of a tetrahedron and $$V1$$ be the volume of another tetrahedron formed by the centroids of faces of the previous tetrahedron and V $$=$$ $$KV1$$ , then K is equal to

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Infinity Learn · Accepted Answer

Consider a tetrahedron with vertices $$O(0$$,$$0$$, $$0)$$, $$A(a$$,$$0$$, $$0)$$, $$B(0$$, b, $$0)$$ and $$C(0$$ , $$0$$, $$c)$$.  Volume $$V=16$$[a→b→c→]Now centroids of the faces OAB, OAC, OBC and ABC arc $$G1(a/3$$, $$b/3$$,$$0)$$, $$G2(3$$,$$0$$, $$c/3)$$, $$G3(0$$, $$b/3$$, $$c/3)$$ and $$G4(a/3$$, $$b/3$$, $$c/3)$$, respectively.$$G4G1=c$$→$$/3$$,$$G4G$$→$$2=b$$→$$/3$$,$$G4G$$→$$3=a$$→$$/3Volume$$ of tetrahedron by centroidsV′$$=16a3b$$→c→$$3=127V$$⇒ $$K=27$$

If V be the volume of a tetrahedron and V¹ be the volume of another tetrahedron formed by the centroids of faces of the previous tetrahedron and V = KV¹ , then K is equal to

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If V be the volume of a tetrahedron and V1 be the volume of another tetrahedron formed by the centroids of faces of the previous tetrahedron and V = KV1 , then K is equal to

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If V be the volume of a tetrahedron and V¹ be the volume of another tetrahedron formed by the centroids of faces of the previous tetrahedron and V = KV¹ , then K is equal to