A carton designer is considering a cost as she is comparing different shaped cartons. Which of these nets would create a cardboard carton that requires the least amount of cardboard for each cubic inch of volume?

Answer:The first option i.e. (8 in × 10 in × 10 in) will be our choice.Step-by-step explanation:Each of the cartons shown here has the same volume i.e. 800 cubic inches. Therefore, the carton having the least surface area will require the least amount of cardboard for each cubic inch of volume. 2(LW + WH + LH) is the surface area of a cuboid with dimensions L × W × H.  Now, in the first option of cardboard with dimension 8 in × 10 in × 10 in, will have surface are = 2(8 × 10 + 10 × 10 + 8 × 10) = 520 sq, inches. Now, in the second option of cardboard with dimension 5 in × 8 in × 20 in, will have surface are = 2(5 × 8 + 8 × 20 + 5 × 20) = 600 sq, inches. Again, in the third option of cardboard with dimension 4 in × 10 in × 20 in, will have surface are = 2(4 × 10 + 10 × 20 + 4 × 20) = 640 sq, inches. Finally, in the fourth option of cardboard with dimension 2 in × 10 in × 40 in, will have surface are = 2(2× 10 + 10 × 40 + 2 × 40) = 1000 sq, inches. Hence, the first option will be our choice. (Answer)