Question

Andy is making paper boxes of different sizes. The supplies are limited; therefore, Andy restricted the volume of each box to 240 cubic inches or less and the base area to exactly 30 square inches. Find the range of the height, h.

Answer 1

The range of the height of the box is 1 inch to 8 inches

Explanation:

Given

Volume of a rectangular box = 240 cubic inches (or less)

Base area of each box = 30 square inches

Required

The range of the height of the box

To calculate the range of the height, we need to get the minimum and maximum height.

Calculating the maximum height

This is attained when the volume of the rectangular box is 240 cubic inches

The volume of a rectangular box is calculated thus

Volume = Base Area * Height

Substituting 240 for volume and 30 for base area; this gives

`240 = 30 * Height`

Divide both sides by 30

`(240)/(30) = (30 * Height)/(30)`

`8 = Height`

`Height = 8 inches`

Hence, the maximum height is 8 inches

Calculating the minimum height

The minimum height is attained when the base area equals the volume.

In other words,

When volume = 30 cubic inches and base area = 30 square inches

Recall that

Volume = Base Area * Height

Substituting 30 for volume and 30 for base area; this gives

`30 = 30 * Height`

Divide both sides by 30

`(30)/(30) = (30 * Height)/(30)`

`1 = Height`

`Height = 1 inch`

Hence, the minimum height is 1 inch

The range of the height of the box is 1 inch to 8 inches