Question

If the maximum number of rectangular boxes of sides 7 cm,6 cm and 4 cm are kept in cubical box of side 33 cm, Then which of the following statements are correct
(A) the number of rectangular boxes which are kept in cubical box is 160.
(B) the volume of remaining place in cubical box is 9057 c. cm.
(C) the volume of the remaining place in cubical box is 9050 c.cm.
(D) the number of rectangular boxes which are kept in cubical box is 214.

Answer 1

Side of Cube $=33$ cm

Length of cuboid $=7$ cm

Breadth of cuboid $=6$ cm

Height of cuboid $=4$ cm

Thus, No. of boxes which can be kept along the length of the cube$=33cm÷7cm=4$

No. of boxes which can be kept along the breadth of the cube$=33cm÷6cm=5$

No. of boxes which can be kept along the height of the cube$=33cm÷4cm=8$

Thus, the total no. of rectangular boxes which can be kept inside the cubical box $=4\times 5\times 8=160$

Volume of one rectangular box $=7cm\times 6cm\times 4cm=168c{m}^3$

$\therefore$ Volume of 160 such boxes $=160\times 168c{m}^3=26880c{m}^3$

Volume of cubical box $=(33cm{)}^3=35937c{m}^3$

So, Volume of remaing place in the cubical box$=9057c{m}^3$

Option A and B are correct.