Use the drawing tool(s) to form the correct answer on the provided number line.
A company manufactures rectangular cardboard boxes. Each box is 20 inches long and 15 inches wide. The heights of the boxes range from 4 to 6 inches.
Plot the range of possible values for the volume of the boxes.
Answer (2)
Calculate the minimum volume using the minimum height: V min = 20 × 15 × 4 = 1200 cubic inches.
Calculate the maximum volume using the maximum height: V ma x = 20 × 15 × 6 = 1800 cubic inches.
Identify the range of possible volumes: from 1200 to 1800 cubic inches.
Represent the range on a number line with a line segment from 1200 to 1800. 1200 to 1800
Explanation
Problem Analysis We are given the dimensions of a rectangular cardboard box: length = 20 inches, width = 15 inches, and height ranging from 4 to 6 inches. Our goal is to find the range of possible volumes for these boxes and represent this range on a number line.
Volume Calculation The volume of a rectangular box is calculated by multiplying its length, width, and height. We need to find the minimum and maximum possible volumes by using the minimum and maximum heights, respectively.
Minimum Volume To find the minimum volume, we use the minimum height of 4 inches: V min = l e n g t h × w i d t h × h e i g h t min = 20 × 15 × 4 = 1200 cubic inches
Maximum Volume To find the maximum volume, we use the maximum height of 6 inches: V ma x = l e n g t h × w i d t h × h e i g h t ma x = 20 × 15 × 6 = 1800 cubic inches
Range Representation The range of possible volumes is from 1200 cubic inches to 1800 cubic inches. To represent this on the number line, we would draw a line segment starting at 1200 and ending at 1800.
Examples
Understanding volume ranges is crucial in logistics and packaging. For instance, when shipping products, knowing the minimum and maximum volume of boxes helps in optimizing storage space and transportation costs. If a company needs to ship items using boxes with the dimensions described, they know that each box will occupy between 1200 and 1800 cubic inches of space. This information is vital for planning and efficient resource allocation.
The volume of the rectangular cardboard boxes can range from 1200 cubic inches to 1800 cubic inches. This is determined by calculating the volume using the box's dimensions and the range of height. The volumes are represented on a number line from 1200 to 1800 cubic inches.
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