Question

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

1. What is the largest cube size that can fit perfectly?
2. What is the volume of the warehouse?
3. What is the volume of the cubical carton?
4. What is the maximum number of cartons that can be stored in the warehouse?

Answer 1

(i)

The edge length of the largest cubical carton is 5.5 m (or 550 cm).

(ii)

\[\text{Volume} = \text{length} \times \text{breadth} \times \text{height} = 88\text{ m} \times 66\text{ m} \times 5.5\text{ m} = 31,944\text{ m}^3\]

(iii)

\[\text{Volume} = (\text{edge})^3 = (5.5\text{ m})^3 = 166.375\text{ m}^3\]

(iv)

\[\text{Number of cartons} = \frac{\text{Volume of the warehouse}}{\text{Volume of one cubical carton}} = \frac{31,944\text{ m}^3}{166.375\text{ m}^3} = 192\]