Question

f volume of a regular tetrahedron of edge length k is V and shortest distance between any pair of opposite edges of same regular tetrahedron is d, then find the value of d^3/V ​

Answer 1

Question :-

If volume of a regular tetrahedron of edge length k is V and shortest distance between any pair of opposite edges of same regular tetrahedron is d, then find the value of d³/V .

SoluTion :-

$\boxed {\sf Volume\ of\ tetrahedron=\frac{k^{3}}{6\sqrt{2} } }$

$\sf {k=Edge\ length= \sqrt{2^{\ .\ }d}}\\\\\\\sf {V=\frac{(d^{\ .\ } \sqrt{2})^{3}}{\sqrt{2}^{\ . \ }6} }$

$\sf {\rightarrowtail \ \frac{\ d^{3}}{V}=3 }$