A warehouse is a large building which, in general, is used to store goods. The dimensions of a warehouse vary with resepct to the goods to be stored.

The dimensions of a particular warehouse are 88 m × 66 m × 5.5 m. Its owner wants to fill it completely with identical cubical cartons of maximum volume.

(i) What is the largest cube size that can fit perfectly ?

(ii) What is the volume of the warehouse ?

(iii) What is the volume of the cubical carton ?

(iv) What is the maximum number of cartons that can be stored in the warehouse ?

Given,

Dimensions of warehouse = 88 m × 66 m × 5.5 m

(i) Largest cube size that can fit = HCF of 88, 66 and 5.5

HCF of 88, 66, 5.5 = 5.5.

Hence, largest cube size that can fit = 5.5 m.

(ii) Volume of warehouse = l × b × h

= 88 × 66 × 5.5

= 31944 m³.

Hence, volume of warehouse = 31944 m³.

(iii) Size of a cubical carton = 5.5 m

Volume of cube = (side)³

= (5.5)³

= 166.375 m³.

Hence, volume of a cubical carton = 166.375 m³.

(iv) Maximum number of cartons that can be stored = $\dfrac{\text{Warehouse volume}}{\text{Cube volume}}$

= $\dfrac{31944}{166.375}$

= 192.

Hence, maximum number of cartons that can be stored in warehouse = 192.