Question

What is the maximum number of whole cuboids of length = 2 cm, breadth = 1 cm and height = 1 cm that can be packed into a larger cuboid of length = 3 cm, breadth = 3 cm and height = 11 cm?

Answer 1

ANSWER :- $\sf \red \boxed { 49 \:whole \:cuboids}$          

       

             SOLUTION  

Maximum number of whole cuboids of length = 2 cm, breadth = 1 cm and height = 1 cm that can be packed into a larger cuboid of length = 3 cm, breadth = 3 cm and height = 11 cm  will be equal to ,

                               

                                                                      $\sf \dfrac{ Volume \;of \:the\: larger \:cuboid}{Volume\: of\: the \:smaller \:cuboid}$

LARGER CUBOID

Length (l) = 3cm

Breadth (b) = 3cm

Height (h) = 11cm

Volume of a Cuboid = l × b × h

Volume of Larger Cuboid = 3 × 3 × 11 = 99 cm³

SMALLER CUBOID

Length (l) = 2cm

Breadth (b) = 1cm

Height (h) = 1cm

Volume of a Cuboid = l × b × h

Volume of Smaller Cuboid = 2 × 1 × 1 = 2cm³

$\sf Number \:of \:Smaller \:Cuboid \:that \:can\: be\: packed\: in \:Larger \:Cuboid = \dfrac{99}{2}$

On Simplification of 99/2 , we will obtain 49.5 , so the larger Cuboid can obtain 49 whole cuboids in it .