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. 120

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 coordinates axes in points A(20, 0, 0), B(0. 15, 0) and C(0, 0, -12) the coordinates of the origin are (0, 0, 0).
$\therefore$ the volume of the tetrahedron O ABC is
$\frac{1}{6}\left|\begin{array}{cccc}0& 0& 0& 1\\ 20& 0& 0& 1\\ 0& 15& 0& 1\\ 0& 0& -12& 1\end{array}\right|=|\frac{1}{6}\times 20\times 15\times (-12\left)\right|=600.$