Question

The volume of the tetrahedrom included between the plane $3x+4y-5z-60=0$ and the coordinate planes is

• A. $60$
• B. $600$
• C. $720$
• D. none of these

Answer 1

The correct option is B $600$

The plane intersect the axes at $(20,0,0),(0,15,0)$ and $(0,0,-12)$

So, the volume of tetragedron $OABC$

$=\frac{1}{6}\left|\begin{array}{cccc}0& 0& 0& 1\\ 20& 0& 0& 1\\ 0& 15& 0& 1\\ 0& 0& -12& 1\end{array}\right|=-\frac{1}{6}\left|\begin{array}{ccc}20& 0& 0\\ 0& 15& 0\\ 0& 0& -12\end{array}\right|=600$