Question

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

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

Answer 1

The correct option is B $600$

Equation of the given plane can be written as
$\frac{x}{20}+\frac{y}{15}+\frac{z}{-12}=1$
Which meets the coordinate axes in points
$A(20,0,0),B(0,15,0),C(0,0,-12)$
and the coordinates of the origin are $(0,0,0)$
$\therefore$ the volume of the tetrahedron $OABC$ is
$\frac{1}{6}\left|\begin{array}{c}0001\\ 20001\\ 01501\\ 00-121\end{array}\right|$ $=|\frac{1}{6}\times 20\times 15\times (-12)|=600$