Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.10 - Modeling with Functions - Concept and Vocabulary Check - Page 291: 3


The length of the box on the right is represented by $10-2x$. Its width is represented by $10-2x$ . Its height is represented by $10-2x$. The volume of the box $V\left( x \right)$ in cubic inches is given by $V\left( x \right)=\left( 10-2x \right)\cdot \left( 10-2x \right)\cdot x$.

Work Step by Step

Consider the statement: $\begin{align} & \text{Length of the square}=15\ \text{inches} \\ & \text{Breadth of the square}=8\ \text{inches} \end{align}$ A machine cuts equal sized squares from each corner, $x$, in inches such that the length and the breadth of the rectangle becomes: $\begin{align} & \text{Length of the square after cutting square, }x\text{, in inches}=10-x-x \\ & =10-2x\text{ } \end{align}$ And $\begin{align} & \text{Breadth of the square after cutting square, }x\text{, in inches}=10-x-x \\ & =10-2x\text{ } \end{align}$ And then the metal is shaped into an open box by turning up the sides. So, $\text{Height of the metal box}=x$ Use the formula: $\text{Volume of the cube}=S\cdot S\cdot S$ Now, the expression for volume (V) of a cube is given by: $V=\left( 10-2x \right)\cdot \left( 10-2x \right)\cdot \left( x \right)$
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