In a rectangular parallelepiped, a section is drawn through the edge of the lower base and the point

In a rectangular parallelepiped, a section is drawn through the edge of the lower base and the point of intersection of the diagonals of the side face. In what relation does the section plane divide the volume of the parallelepiped?

Point O is the intersection point of the diagonals of the lateral face, then the MK segment passing through the point O divides the lateral faces in half.

Let the dimensions of the parallelepiped be a, b, cm. Then its volume will be equal to: V1 = a * b * c cm3.

Let’s construct a cross-section of the РНCM, which divides the volume of the parallelepiped in half.

V2 = V1 / 2 = a * b * c / 2 cm3.

Then the section ABKM is the diagonal section of the parallelepiped ABCDРНM, which also divides its volume in half.

V3 = V2 / 2 = V1 / 4 = a * b * c / 4 cm3.

Then the volume of the truncated prism ABKMA1B1С1D1 is: V4 = V1 – V3 = 3 * a * b * c / 4.

V3 / V4 ratio = (1/4) / (3/4) = 1/3.

Answer: The section divides the volume by 1/3.