Multiple choice

The volume of a rectangle block of stone is $10368d{m^3}$. Its dimensions are in the ratio $3:2:1$. If its entire surface is polished at $2$ paise per $d{m^2}$, then the total cost will be

  1. $Rs \ 31.50$
  2. $Rs \ 31.68$
  3. $Rs \ 63$
  4. $Rs \ 63.36$
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D Correct answer
Explanation

Let the dimensions be 3x, 2x, and x. Since 6x^3 = 10,368, x = 12 dm, giving dimensions 36 dm, 24 dm, and 12 dm. The total surface area is 3,168 dm^2, and at 2 paise per dm^2 the cost is Rs. 63.36.

AI explanation

Let the dimensions of the block be 3x, 2x, and x. Using the volume formula, 6x^3 = 10368, which simplifies to x^3 = 1728, so x is 12 and the dimensions are 36 dm, 24 dm, and 12 dm. The total surface area formula 2*(lb + bh + hl) gives 2*((36*24) + (24*12) + (12*36)) = 2*(864 + 288 + 432) = 3168 dm^2. Multiplying this area by the polishing rate of 2 paise per dm^2 gives a total cost of 6336 paise. Converting paise to rupees by dividing by 100 gives Rs 63.36. The result is Rs 63.36.

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