A carton designer is considering 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?.
Answers
A carton designer is considering cost as she is comparing different shaped cartons. The nets would create a cardboard carton that requires the least amount of cardboard for each cubic inch of volume is (8 in × 10 in × 10 in). the first option is the correct answer.
Each of the containers in this image is 800 cubic inches in volume.
As a result, for every cubic inch of volume, the carton with the smallest surface area will use the least quantity of cardboard.
The surface area of a cuboid with the dimensions L, W, and H is equal to 2(LW, WH, and LH).
Now, the first cardboard choice, which has dimensions of 8 in. x 10 in. x 10 in., will have a surface area of 2(8 × 10 + 10 × 10 + 8 × 10) = 520 sq, inches.
Now, the surface area of the cardboard in the second choice, which has dimensions of 2(5 × 8 + 8 × 20 + 5 × 20) = 600 sq, inches.
Once more, the third option's cardboard, which has dimensions of 2(4 × 10 + 10 × 20 + 4 × 20) = 640 sq, inches.
Finally, the cardboard in the fourth option, which has dimensions of 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
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[tex]F \infty \dfrac{1}{\Big (\dfrac{r}{2} \Big)^2}[/tex]
[tex]F \infty \dfrac{4}{r^2}[/tex]
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