Multiple choice

The dimensions of a solid metal cuboid are $\displaystyle 72cm\times 30cm\times 75cm.$ It is melted and recast into indentical solid metal cubes with edge of each 6 cm. Find the number of cubes formed. Also, find the cost of polishing the surfaces of all cubes formed at the rate Rs. 150 per sq. m.

  1. $710$; Rs.$ 2,430$
  2. $790$; Rs. $2,430$
  3. $740$; Rs.$ 2,430$
  4. $750$; Rs. $2,430$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Number of cubes = (72*30*75) / (6^3) = 162000 / 216 = 750. Surface area of one cube = 6 * 6^2 = 216 cm^2 = 0.0216 m^2. Total surface area = 750 * 0.0216 = 16.2 m^2. Cost = 16.2 * 150 = 2430.

AI explanation

The number of cubes formed is the total volume of the cuboid divided by the volume of one small cube, which is (72 * 30 * 75) / 6^3 = 162000 / 216 = 750 cubes. The total surface area to be polished is 750 multiplied by the surface area of one cube, giving 750 * 6 * 6^2 = 162000 cm^2. Converting this to square meters gives 16.2 m^2, and multiplying by the rate of Rs. 150 per m^2 results in a cost of Rs. 2,430.

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