Question

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

Answer 1

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  $\times$ 1.55 =  26.35

And, 26.35 < 27.5

Therefore, 17 discs can definitely fit in the box.