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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.
Solution
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
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