Question

The internal length, breadth, and height of a box are 30 cm, 24 cm, and 15 cm. Find the largest number of cubes which can be placed inside this box if the edge of each cube is
(i) 3 cm (ii) 4 cm (iii) 5 cm

Answer 1

(i) No. of the cube which can be placed along the length = `(30)/3` =10.

No. of the cube along with the breadth = `(24)/3` = 8

No. of cubes along with the height = `(15)/3` =5.

∴ The total no. of cubes placed = 10 x 8 x 5 = 400

(ii) Cubes along length = `(30)/4` = 7.5 = 7.

Cubes along width = `(24)/4` = 6 and cubes along with height =`( 15 )/4` = 3.75 = 3

∴ The total no. of cubes placed = 7 x 6 x 3 = 126

(iii) Cubes along length = `(30)/5` = 6 

Cubes along width = `(24)/( 5 )` = 4 . 5 = 4 and cubes along with height = `( 15 ) / ( 5 )` =3 

∴ The total no. of cubes placed = 6 x 4 x 3 = 72