Discussion Forum

1)

The volume of the tetrahedron (in cubix units)  formed by the plane 2x+y+z=K

 and the coordinate planes is $\frac {2V^{3}}{3}$ , then K:V=

Answer:

Option D

Explanation:

  Equation of given plane is 

      $2x+y+z=K$           ........(i)

Point of intersection of plane  (i) with the coordinate axes is A ($\frac{K}{2},0,0$), B(0,K,0)  and C(0,0,K).

 Now , volume of the tetrahedron 0ABC

  = $\frac{1}{6}$  [OA OB  OC]=   $\frac{1}{6}\begin{bmatrix}\frac{K}{2} & 0& 0\\0 & K&0\\0&0&K \end{bmatrix}= \frac{2V^{3}}{3}$        (given)

  $\Rightarrow$     $\frac{1}{6} \frac {K^{3}}{2}= \frac{2V^{3}}{3}$

 $\Rightarrow$   $\left(\frac{K}{V}\right)^{3}=2^{3}\Rightarrow K:V=2:1$