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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.
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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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