Question

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

• A. $60$
• B. $600$
• C. $720$
• D. $400$

Answer 1

Answer: (B)

$600$

The given equation of the plane is $3x+4y-5z-60=0$.

It can be written in the form $\frac{x}{20}+\frac{y}{15}+\frac{z}{-12}=1$ x20+y15+z−12=1
which meets the coordinate axes at the points $A(20,0,0),B(0,15,0)$ and $C(0,0,-12)$.
The coordinates of the origin are $O(0,0,0)$.
Therefore, volume of the tetrahedron $OABC$ is

$=\frac{1}{6}\left|\begin{array}{ccc}20& 0& 0\\ 0& 15& 0\\ 0& 0& -12\end{array}\right|=\frac{3600}{6}=600$
Hence, option B is correct.