Questions: A cardboard box used for flat rate shipping by a postal service has length 18 inches, width 14 inches, and height 7 inches. Complete parts a through d below. a. The volume of a rectangular box is the product of the length times the width times the height. Determine the volume of the box. The volume of the box is 1764 cubic inches. (Simplify your answer.) b. Suppose each dimension is increased by x inches. Represent the length, width, and height of the new box symbolically in terms of x. The length of the new box in terms of x is 18+x. The width of the new box in terms of x is 14+x.

A cardboard box used for flat rate shipping by a postal service has length 18 inches, width 14 inches, and height 7 inches. Complete parts a through d below. a. The volume of a rectangular box is the product of the length times the width times the height. Determine the volume of the box. The volume of the box is 1764 cubic inches. (Simplify your answer.) b. Suppose each dimension is increased by x inches. Represent the length, width, and height of the new box symbolically in terms of x. The length of the new box in terms of x is 18+x. The width of the new box in terms of x is 14+x.
Transcript text: Save A cardboard box used for flat rate shipping by a postal service has length 18 inches, width 14 inches, and height 7 inches. Complete parts a through d below. a. The volume of a rectangular box is the product of the length times the width times the height. Determine the volume of the box. The volume of the box is 1764 cubic inches. (Simplify your answer.) b. Suppose each dimension is increased by $x$ inches. Represent the length, width, and height of the new box symbolically in terms of $x$. The length of the new box in terms of $x$ is $18+x$. The width of the new box in terms of x is $\square$.
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Solution

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Solution Steps

Step 1: Calculate the Volume of the Box

The volume \( V \) of a rectangular box is given by the product of its length \( l \), width \( w \), and height \( h \).

Given:

  • Length \( l = 18 \) inches
  • Width \( w = 14 \) inches
  • Height \( h = 7 \) inches

\[ V = l \times w \times h \] \[ V = 18 \times 14 \times 7 \] \[ V = 1764 \text{ cubic inches} \]

Step 2: Represent the Length of the New Box in Terms of \( x \)

Suppose each dimension is increased by \( x \) inches. The new length \( l' \) of the box is:

\[ l' = 18 + x \]

Step 3: Represent the Width of the New Box in Terms of \( x \)

The new width \( w' \) of the box is:

\[ w' = 14 + x \]

Final Answer

  1. The volume of the box is \( 1764 \) cubic inches.
  2. The length of the new box in terms of \( x \) is \( 18 + x \).
  3. The width of the new box in terms of \( x \) is \( 14 + x \).
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