A cuboidal block of metal has dimensions 36 cm by 32 cm by 0.25 m. It is melted and recast into cubes with an edge of 4 cm.

(i) How many such cubes can be made?

(ii) What is the cost of silver coating the surfaces of the cubes at the rate of ₹1.25 per square centimeter?

(i) Given,

Dimensions of cuboidal block = 36 cm, 32 cm and 0.25 m.

Volume of cuboidal box = 36 cm × 32 cm × (0.25 × 100) cm

= (36 × 32 × 25) cm³

= 28800 cm³.

Volume of cube having edge 4 cm = 4 × 4 × 4 = 64 cm³.

We know that,

Number of cubes = $\dfrac{\text{Volume of cuboidal block}}{\text{Volume of one cube}}$

$= \dfrac{28800}{64} \\[1em] = 450$

Hence, 450 cubes can be made.

(ii) By formula,

Total surface area of one cube = 6(side)²

= 6.(4)²

= 6 × 4 × 4

= 96 cm².

So, the total surface area of 450 cubes = 450 × 96 = 43200 cm²

Cost of silver coating the surface for 1 cm² = ₹1.25

Cost of silver coating the surface for 43200 cm² = 43200 × 1.25 = ₹54000.

Hence, cost of silver coating the surface of cube = ₹54000.