Question

The dimensions of a solid metallic cuboid are 72 cm × 30 cm × 75 cm. It is melted and recast into identical solid metal cubes with each edge 6 cm. Find the number of cubes formed.

Also, find the cost of polishing the surfaces of all the cubes formed at the rate Rs. 150 per sq. m.

Answer 1

The dimensions of a solid are: 72 cm, 30 cm, 75 cm
The volume of the cuboid = 72 cm x 30 cm x 75 cm = 162000 cm³
Side of a cube = 6 cm 
Volume of a cube = 6³ = 216 cm³

The number of a cube = ` (162000)/(216) = 750`

The surface area  of  a cube = 6a² = 6 x 6² = 216 cm²
Total surface area of 750 cubes = 750 x 216 = 162000 cm²

Total surface area in square metres = `(162000)/(10000)`
                                                        = 16.2 square meters

Rates of polishing the surface per square meter = Rs. 150

The total cost of polishing the surface = 150 x 16.2 = Rs. 2430