Question

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.

Question 4 options:

Answer 1

(a)18.85 Cubic Inches

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

Explanation:

Part A

Height =2 Inches

Diameter=1 Inch

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

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

Volume of 1 Container
`=\pi* 0.5^2*2= 0.5\pi $ cubic inches`

Volume of the 12 Containers
`=12*0.5\pi =18.85$ cubic inches`

Part B

Next, we determine the container that should be used. Let us first determine the volume of each of the boxes available for easy comparison.

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 volume of the 12 film containers is greater than 18 but less than 24. Therefore,the box that should be used with the least amount of wasted space is the box with a volume of 24 Cubic inches.