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.

Answer 1

Answer:

(a)18.85 cubic inches

(b)Box with dimension 4 in. x 3in. x 2 in

Step-by-step explanation:

Volume of Film Containers

Diameter=1 inch,

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

Height =2 Inches

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

Volume of 1 container$=\pi *0.5^2*2=\frac{\pi}{2} \:cubic \: inches$

Volume of 12 containers$=12*\frac{\pi}{2} =18.85\:cubic \: inches$

Volume of Boxes

• 3 in. x 2 in. x 5 in.=30 cubic inches
• 4 in. x 3in. x 2 in.=24 cubic inches
• 5 in. x 6 in. x 5 in.=150 cubic inches
• 3 in. x 2 in. x 3 in=18 cubic inches

(B)The box with dimension of 4 in. x 3in. x 2 in. should be used to fit a dozen film containers with the least amount of wasted space since its volume is the next greater than that of the 12 containers combined. Any box with an higher volume will increase the space wasted.

The box with a volume of 18 cubic inches cannot be used since its volume is lesser than the combined volume of the containers.