Question

A box is a cuboid with dimensions 26cm by 15cm by 20cm all measured to the nearest cm. Disc cases are cuboids which measure 1.6cm by 14.2cm by 19.3cm all measured to the nearest millimetre. If the disc cases are stacked as shown, show that ur may not be possible for 16 cases to fit in the box

Answer 1

Explanation:

We may not be able to fit 16 cases in the box because their combined volume will be greater than the box which will make it impossible.

The dimensions of the big box is given as:

Length= 26 cm

Breadth= 15 cm

Height= 20 cm

So its volume can be calculated by:

Volume= Length x Breadth x Height

Volume= 26 cm x 15 cm x 20 cm

Volume1= 7800 cm³

Now, the dimension of one disc case is given as:

Length= 1.6 cm

Breadth= 14.2 cm

Height= 19.3 cm

The volume of one disc case will be:

Volume= 1.6 cm x 14.2 cm x 19.3 cm

Volume= 438.496 cm³

So, volume of 16 disc cases= 16 X volume of one disc case

Volume2= 16 x 438.496 cm³

Volume2= 7015.936 cm³

Since Volume1 < Volume2

So, 16 disc cases cannot be fit into a box.