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Plane cuts cuboid, calculate volume of blocks

Source: XIII Polish Junior MO 2018 First Round - Problem 7

April 24, 2018

3D geometrysquareVolumePolandPlanegeometry

Problem Statement

Square

ABCD

with sides of length

4

is a base of a cuboid

ABCDA'B'C'D'

. Side edges

AA'

BB'

CC'

DD'

of this cuboid have length

7

. Points

K, L, M

lie respectively on line segments

AA'

BB'

CC'

, and

AK = 3

BL = 2

CM = 5

. Plane passing through points

K, L, M

cuts cuboid on two blocks. Calculate volumes of these blocks.