A box is a cuboid with dimensions 28 cm by 15 cm by 20 cm all measured to the nearest centimetre.
Disc cases are cuboids which measure 1.5 cm by 14.2 cm by 19.3 cm all
measured to the nearest millimetre.
Show that 17 disc cases, stacked as shown, will definitely fit in the box.
19.3 cm
ㅋ
20 cm
15 cm
14.2 cm
28 cm
1.5 cm

Step-by-step explanation:

The dimensions of the box as given is

28 by 15 by 20.

Therefore writing the lower bound and the higher bound for the box dimensions respectively are --

Box :

Length (27.5 , 28.5)

Width (14.5 , 15.5)

Height (19.5 , 20.5)

Similarly writing the disc dimensions with their lower and higher bounds respectively as --

Disc :

Length (1.45 , 1.55)

Width (14.25 , 14.35)

Height (19.25, 19.35)

Therefore, using the lower bounds of the box and the upper bounds of the discs,

14.35 < 14.5

19.35 < 19.5

So, 17   1.55 =  26.35

And, 26.35 < 27.5

Therefore, 17 discs can definitely fit in the box.

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