Question

Find the maximum number of cubical boxes of side 5 cm, which can be accommodated
in a carton of dimensions 25 cm x 10 cm x 15 cm.​

Answer 1

Answer:

We have to calculate the number of boxes that can be fit into the carton of dimensions 15×9×12

By these dimensions ..this is clear that it is a cubiodal carton….

And number of boxes which are going to fit in this can be calculated by the concept of volume of both …the cubical boxes and the cuboidal carton…

First you have to know the volume of cubiod and cube..

The volume of cuboid =length×base×hieght

And the volume of cube=length ×length×length

Now,

Volume of cuboidal carton will be=l×b×h

That is ….15×9×12=1620cm^3

And that the volume of the cubical box=l×l×l

That is….3×3×3=27cm^3

Now the number of cubical boxes that can be fit into the cubiodal carton will be=(volume of cuboidal carton)÷(volume of one cubical box)

=>1620÷27=60 boxes

Hence 60 boxes can be fit into that cuboidal carton…

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Step-by-step explanation:

Answer 2

Given:

• Each side of the cubical box 5 cm
• The dimensions of the carton are 25cm×10cm×15cm

To find:

The maximum number of cubical boxes of side 5cm that can be accommodated in a carton of dimensions 25cm×10cm×15cm

So,

The volume of the carton of dimensions 25cm×10cm×15cm is

= lbh unit cube

[In which 'l' is 'length', 'b' is 'breadth', and 'h' is 'height']

= 25 × 10 × 15

= 3750 cm cube

Now,

The volume of 1 cubical box of side 5cm is

= (side)³ unit cube

= (5)³

= 125 cm cube

Now,

$\bf Number\ of\ cubes = \frac{Volume\ of\ carton}{Volume\ of\ each\ cubical\ box}$

$\bf Number\ of\ cubes = \frac{3750}{125}$

Number of cubes = 30

Hence,

Maximum 30 such cubical boxes of side 5cm is needed that can be accommodated in a carton of dimensions 25 cm x 10 cm x 15 cm.