Beverly needs to make a container in the shape of a rectangular prism that holds 1000 in3 of liquid. The height of the container must be 10 in. She wants to use the dimensions that will allow her to use the least amount of material possible. Beverly's mother says the difference in the amount of material will be too minor to worry about. Beverly believes it is possible to save more than half the material needed if they pick the right dimensions. Who is correct? Support your answer with specific numbers, and explain your reasoning. The dimensions are measured in whole units.

Question

Mathematics

Maurice Stevenson

5 October, 21:17

Beverly needs to make a container in the shape of a rectangular prism that holds 1000 in3 of liquid. The height of the container must be 10 in. She wants to use the dimensions that will allow her to use the least amount of material possible. Beverly's mother says the difference in the amount of material will be too minor to worry about. Beverly believes it is possible to save more than half the material needed if they pick the right dimensions. Who is correct? Support your answer with specific numbers, and explain your reasoning. The dimensions are measured in whole units.

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Answers (1)

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Sassafras · Answer 1

Given:

volume = 1,000 in³

height = 10 in

1,000 in³ / 10 in = 100 in² Area.

100 in²

Length Width Surface Area of the Rectangular prism

100 in 1 in 2,220 in²

50 in 2 in 1,240 in²

25 in 4 in 780 in²

20 in 5 in 700 in²

Surface area = 2 (wl + hl + lw)

The best dimension is 20 inches by 5 inches by 10 inches. It has lesser surface area than other dimensions. Thus, it can save more materials.