Question

The length, breadth and height of a pencil box are 15cm, 8cm and 3cm respectively. How
many such boxes can be packed in a cubical box of 1.2m long ?​

Answer 1

❍ Let the no.of.boxes be x boxes respectively.

$\\ \underline{\bigstar\;\boldsymbol{Concept:-}}$

• Here,the length,breadth and height of a pencil box are 15 cm,8 cm, and 3 cm.So the pencil box must be in cuboid shape and the boxes can be packed in a cubical box of 1.2 long is side ,so the small boxes must be in cube shape.Then the formula's to use are volume of cuboid,volume of cube and (volume of cuboid/volume of cube) to find the no.of.boxes.

$\\ \underline{\dag\;\frak{Formula's:}}\\ \\ \\ \sf{Volume\; of \;cuboid = lbh}\\ \\ \sf{ Volume\; of \;cube = a^3}\\ \\ \sf{No.of.box=\frac{Volume\; of \;cube}{Volume\; of \;cuboid}}$

Applying the values,

$\\ \longrightarrow\;\sf{Volume\;of\;cuboid=15\times 8\times 3}\\ \\ \longrightarrow\;\sf{Volume\;of\;cuboid= 360\;cm^3}$

Converting 1.2 m to cm

1 m = 100 cm

1.2 m = 1.2 × 100

1.2 m = 120 cm

$\\ \longrightarrow\;\sf{Volume\;of\;cube = (120)^3}\\ \\ \longrightarrow\;\sf{Volume\;of\;cube = 17,28,000\;cm^3}$

Now,finding the no.of.boxes

$\\ \dashrightarrow\;\sf{x= \frac{\cancel{1728000}}{\cancel{360}}}\\ \\ \dashrightarrow\;\sf{x=4800\; boxes}$

Hence,

• 4800 boxes can be packed in a cubical box.