Mathematics
The dimensions of a solid metallic cuboid are 72 cm x 30 cm x 75 cm. It is melted and recast into identical solid metal cubes with each of 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 ₹ 150 per sq.m.
Mensuration
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Answer
Given:
Dimensions of the solid cuboid = 72 cm x 30 cm x 75 cm
Side of the cube = 6 cm
Let n be the number of cubes.
Volume of solid cuboid = Number of cubes x Volume of one cube
⇒ l x b x h = n x side3
⇒ 72 x 30 x 75 = n x (6)3
⇒ 162,000 = n x 216
⇒ n =
⇒ n = 750
Total surface area of one cube = 6 x side2
= 6 x (6)2 cm2
= 216 cm2
Total surface area of 750 cubes = 750 x 216 cm2
= 162,000 cm2
= 16.2 m2
Rate of polishing = ₹ 150 per sq.m
Total cost = Total surface area x Rate of polishing
= ₹ 16.2 x 150
= ₹ 2,430
Hence, the number of cubes formed = 750 and the total cost of polishing = ₹ 2,430.
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