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Question

A tetrahedron (T1) has a fixed volume, V1. Another tetrahedron (T2) with volume V2 is drawn by joining the centroids of the faces of T1. If V1=kV2, then the value of k is

A
92
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B
18
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C
27
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D
9
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Solution

The correct option is C 27
Let the vertices of T1 are O(0,0,0), A(a,0,0), B(0,b,0) and C(0,0,c)
Now, centroids of faces of T1
i.e., OAB, OAC, OBC and ABC are P(a3,b3,0), Q(a3,0,c3), R(0,b3,c3) and S(a3,b3,c3) respectively.
PS=c3, QS=b3, RS=a3
V1=16[abc]V2=16a3b3c3=127×6[abc]k=27

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