Multiple choice

A dairy farm produces rectangular milk cartons for packaging milk. The dimensions of a carton are in the ratio of 5 : 4 : 3 (length : width : height). If the volume of one such carton is 480 cubic decimeters (dm3), determine the cost of laminating the entire outer surface of the carton at the rate of 3 cents per square decimeter (dm2).

  1. $8.90
  2. $10.28
  3. $11.28
  4. $13.76
  5. $14.36
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C Correct answer
Explanation

Let dimensions be 5x, 4x, 3x. Volume = 60x^3 = 480, so x^3 = 8, x = 2. Dimensions are 10, 8, 6. Surface area = 2(10*8 + 8*6 + 6*10) = 2(80 + 48 + 60) = 2(188) = 376 dm^2. Cost = 376 * 0.03 = 11.28.

AI explanation

Let the dimensions of the carton be 5x, 4x, and 3x, so the volume is 5x times 4x times 3x, which equals 60x cubed. Setting the volume equal to 480 cubic decimeters gives 60x cubed equals 480, meaning x cubed equals 8 and x equals 2, making the dimensions 10 dm, 8 dm, and 6 dm. The total surface area of a cuboid is calculated as 2 times (length times width plus length times height plus width times height), which becomes 2 times (10 times 8 plus 10 times 6 plus 8 times 6), yielding 376 square decimeters. Multiplying this surface area by the lamination cost of 3 cents per square decimeter gives 1128 cents, which converts to $11.28.

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