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

(i) Given:

Dimensions of box = 30 cm x 24 cm x 15 cm

Edge of cube = 3 cm

Number of cubes which can be placed along length = $\dfrac{30}{3}$ = 10

Number of cubes which can be placed along breadth = $\dfrac{24}{3}$ = 8

Number of cubes which can be placed along height = $\dfrac{15}{3}$ = 5

The total number of cubes placed = 10 x 8 x 5 = 400

Hence, the number of cubes = 400.

(ii) Given:

Dimensions of box = 30 cm x 24 cm x 15 cm

Edge of cube = 4 cm

Number of cubes which can be placed along length = $\dfrac{30}{4}$ = 7.5 = 7 (taking only integer value)

Number of cubes which can be placed along breadth = $\dfrac{24}{4}$ = 6

Number of cubes which can be placed along height = $\dfrac{15}{4}$ = 3.75 = 3 (taking only integer value)

The total number of cubes placed = 7 x 6 x 3 = 126

Hence, the number of cubes = 126.

(iii) Given:

Dimensions of box = 30 cm x 24 cm x 15 cm

Edge of cube = 5 cm

Number of cubes which can be placed along length = $\dfrac{30}{5}$ = 6

Number of cubes which can be placed along breadth = $\dfrac{24}{5}$ = 4.8 = 4 (taking only integer value)

Number of cubes which can be placed along height = $\dfrac{15}{5}$ = 3

The total number of cubes placed = 6 x 4 x 3 = 72

Hence, the number of cubes = 72.