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MHT CET202618 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

If the plane 2x + 3y + z = 6 cuts coordinate axes at A, B and C, then the volume of tetrahedron OABC (where O is the origin) is ......cubic units.

Options

  1. A30
  2. B6
  3. C36
  4. D180

Correct answer

B. 6

Step-by-step solution

The equation of the plane is 2x + 3y + z = 6 . Dividing by 6 , the intercept form of the plane is x 3 + y 2 + z 6 = 1 . The intercepts on the coordinate axes are a = 3 , b = 2 , and c = 6 . The coordinates of the vertices of the tetrahedron are A(3, 0, 0) , B(0, 2, 0) , and C(0, 0, 6) , with O(0, 0, 0) as the origin. The volume of the tetrahedron OABC is given by V = 1 6 abc . Substituting the values, V = 1 6 (3)(2)(6) = 6 cubic units. Answer: 6

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