Mathematics, 04.05.2020 23:58 jtswagg6634

You work part-time at the “Pack-it and Mail-it” that sells containers used for shipping items. Your photography teacher asks you to recommend the best package to ship 35 mm film containers. The film containers are 1 inch in diameter and 2 inches in height, and they are to be shipped in groups of twelve.

A) Find the volume of twelve film containers. Round your result to two decimal places and show all calculations below.

B) Which container should be used to fit a dozen film containers with the least amount of wasted space? Explain your reasoning.

At work you get a list of package sizes. Your store has four box sizes that look like they might work. The sizes are given in the form l x w x h. They are 3 in. x 2 in. x 5 in., 4 in. x 3in. x 2 in., 5 in. x 6 in. x 5 in., and 3 in. x 2 in. x 3 in.

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Answer from: alexandria3498

(a)18.85 Cubic Inches

(b)The box with dimensions of 4 in. x 3in. x 2 in.

Step-by-step explanation:

Part A

Volume of the 12 Containers

Height =2 Inches

Diameter=1 Inch

Radius=Diameter/2=1/2=0.5 Inch

Volume of a cylinder $=\pi r^2 h$

Volume of the 12 Containers

$=12 X \pi r^2 h\\=12 X\pi X0.5^2X2\\=6\pi $ cubic inches\\=18.85 \text{cubic inches (to two decimal places)}$

Part B

To determine the container which should be used, we first determine the volume of the available boxes.

Volume of the boxes

Volume of box with dimension 3 in. x 2 in. x 5 in.=3X2X5=30 Cubic Inches

Volume of box with dimension 4 in. x 3in. x 2 in.=4X3X2=24 Cubic Inches

Volume of box with dimension 5 in. x 6 in. x 5 in.=5X6X5=150 Cubic Inches

Volume of box with dimension 3 in. x 2 in. x 3 in. =3X2X3=18 Cubic Inches

The box that should be used with the least amount of wasted space is he box with volume 24 Cubic inches. i.e. box with dimensions 4 in. x 3in. x 2 in.

This is because the volume of the box(18 cubic inches) with dimension 3 in. x 2 in. x 3 in. is less than what is required.

Answer from: Quest

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6

step by step explanation:

1/3 + 1/3 = 2/3 2/3=4/6

Answer from: Quest

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a. $y = 60(1) - 90 \\ y = 60 - 90 \\ y = - 30$ this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b. $y = 60(1) - 150 \\ y = 60 - 150 \\ y = - 90$ this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )

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