Chapter 4.5, Problem 11CFU

(a)

To determine

To write: A polynomial function that models the volume of the new box.

Answer to Problem 11CFU

  $x^3+60x^2+1025x+3750$

Explanation of Solution

Given information: Manufacturing: The It’s A Snap Puzzle Company is designing new boxes for their 2000 piece 3-D puzzles. The old box measured 25 centimeters by 30 centimeters by 5 centimeters. For the new box, the designer wants to increase each dimension by a uniform amount.

Calculation:

Increasing each dimension by a uniform amount gives:

  $\begin{array}{l}\left(25+x\right)\left(30+x\right)\left(5+x\right)\\ \Rightarrow x^3+60x^2+1025x+3750\end{array}$

(b)

To determine

To write: An equation that models the situation in which the volume of the new box must be 1.5 times the volume of the old box to hold the increase in puzzle pieces.

Answer to Problem 11CFU

  $x^3+60x^2+1025x+3750=5625$

Explanation of Solution

Given information: Manufacturing: The It’s A Snap Puzzle Company is designing new boxes for their 2000 piece 3-D puzzles. The old box measured 25 centimeters by 30 centimeters by 5 centimeters. For the new box, the designer wants to increase each dimension by a uniform amount.

Calculation:

  $\begin{array}{l}{x}^3+60x^2+1025x+3750\\ \to x^3+60x^2+1025x+3750=5625\end{array}$

(c)

To determine

To find: The dimensions of the new box.

Answer to Problem 11CFU

The dimensions of the new box are approx.: $6.66\times 26.66\times 31.66$

Explanation of Solution

Given information: Manufacturing: The It’s A Snap Puzzle Company is designing new boxes for their 2000 piece 3-D puzzles. The old box measured 25 centimeters by 30 centimeters by 5 centimeters. For the new box, the designer wants to increase each dimension by a uniform amount.

Calculation:

  $x^3+60x^2+1025x-1875=0$

  

xappears to be 1.66cm.

Therefore the dimensions of the new box are approx.: $6.66\times 26.66\times 31.66$