Question

Rolled oats (dry oatmeal) come in cylindrical containers with a diameter of 5 inches and a height of 9.5 inches. These containers are shipped to grocery stores in rectangular prism-shaped boxes. Each shipping box contains six rolled oats containers. The shipping company is trying to figure out the dimensions of the box for shipping the rolled oats containers that will use the least amount of cardboard. They are only considering boxes that are rectangular prisms so that they are easy to stack.

What dimensions of the box would you recommend to the company (length, width, height)?

a) Length: 20 inches, Width: 15 inches, Height: 9.5 inches.
b) Length: 10 inches, Width: 5 inches, Height: 4.75 inches.
c) Length: 9.5 inches, Width: 5 inches, Height: 20 inches.
d) Length: 9.5 inches, Width: 5 inches, Height: 10 inches.

Answer 1

The best dimensions for the least amount of cardboard to ship the cylindrical containers would be a length of 15 inches, a width of 9.5 inches, and a height of 5 inches.

Step-by-step explanation:

To determine the dimensions of the box that will use the least amount of cardboard to ship six cylindrical containers of rolled oats, we need to consider the dimensions of the containers and the arrangement that will most efficiently use the space of a rectangular prism-shaped box.

The containers have a diameter of 5 inches and a height of 9.5 inches. If we stand three containers next to each other, the total width would be 5 inches x 3 = 15 inches. If we then stack two layers of these three containers, the length of the box would be the same as the height of the cylinders, which is 9.5 inches. The height of the container would be 5 inches, which is the diameter of one container. This arrangement would result in two layers of three containers each, fitting snugly into the box. Therefore, the dimensions of the rectangular box that would use the least amount of cardboard while fitting all six containers would be a length of 15 inches, a width of 9.5 inches, and a height of 5 inches.