Question

Jason is designing the packaging for a new brand of snack crackers. To fit on shelves, the package must not be more than 8 1/2 inches tall. The company wants the base of the package to be squared so that it stands out of its competitors. The box must be able to hold 100 cubic units of crackers. Which could be the dimensions for Jason's design?

Answer 1

Explanation:

8 1/2 inches =
`(17)/(2)` inches

To fit on shelves, the package must not be more than 8 1/2 inches tall, it means the height of the package can be at
`(17)/(2)` inches

The box must be able to hold 100 cubic units of crackers. it means the volume of the box is 100 cubic units.

The base of the package to be squared

And we have the formula:

V = h*S (Area of the base)

=> S = V/h = 100 :
`(17)/(2)` =
`(200)/(17)`

=> the side of square:
`\sqrt{(200)/(17) }`

The dimensions for Jason's design are:

The height:
`(17)/(2)` inches

The length and width:
`\sqrt{(200)/(17) }`