7

Part of 2018 Polish Junior MO First Round

Problems(1)

Plane cuts cuboid, calculate volume of blocks

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

ABCD

with sides of length

4

is a base of a cuboid

ABCDA'B'C'D'

AA'

BB'

CC'

DD'

of this cuboid have length

7

K, L, M

lie respectively on line segments

AA'

BB'

CC'

AK = 3

BL = 2

CM = 5

. Plane passing through points

K, L, M

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

3D geometrysquareVolumePolandPlanegeometry