(i) How many cubic cm of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout ?

(ii) If 1 cm³ of iron weighs 15 g, find the weight of the empty box in kg.

(i) Given,

External dimensions :

Length (L) = 36 cm

Breadth (B) = 25 cm

Height (H) = 16.5 cm

Internal dimensions:

Since the thickness = 1.5 cm

∴ Length (l) = 36 - (1.5 + 1.5) = 36 - 3 = 33 cm

Breadth (b) = 25 - (1.5 + 1.5) = 25 - 3 = 22 cm

Height (h) = 16.5 - 1.5 = 15 cm (Since, box is open)

Calculating the external volume,

Volume = L × B × H

= 36 × 25 × 16.5

= 14,850 cm³.

Calculating internal volume,

Volume = l × b × h

= 33 × 22 × 15

= 10,890 cm³

Calculating volume of iron,

Volume of iron = External volume - Internal volume

= 14,850 - 10,890

= 3,960 cm³.

Hence, volume of iron = 3,960 cm³.

(ii) Given,

Weight of iron = 15 g

Total weight of the box = Volume of iron × weight of iron.

= 3,960 × 15 g

= 59,400 g.

1000 g = 1 kg

∴ 59,400 g = $\dfrac{59,400}{1000}$ kg

= 59.4 kg

Hence, weight of the box = 59.4 kg.