Question

$A$ cardboard box has a square base, with each edge of the base having length $x$ inches, as shown in the figure. The total length of all 12 edges of the box is 144 in. (a) Show that the volume of the box is given by the function $V(x)=2 x^{2}(18-x)$ (b) What is the domain of $V$ ? (Use the fact that length and volume must be 2 (c) Draw a graph of the function $V$ and use it to estimate the maximum volume for such a box. (FIGURE CAN NOT COPY)

          $A$ cardboard box has a square base, with each edge of the base having length $x$ inches, as shown in the figure. The total length of all 12 edges of the box is 144 in.
(a) Show that the volume of the box is given by the function $V(x)=2 x^{2}(18-x)$
(b) What is the domain of $V$ ? (Use the fact that length and volume must be 2
(c) Draw a graph of the function $V$ and use it to estimate the maximum volume for such a box.
(FIGURE CAN NOT COPY)

Added by Lisa J.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Supreeta N

08/08/2023

Step 1

There are 12 edges in total, and 4 of them are the edges of the square base, each with length $x$. The remaining 8 edges are the heights of the box. Since the total length of all 12 edges is 144 inches, we have: $4x + 8h = 144$ Solving for $h$, we get: $h = Show more…

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$A$ cardboard box has a square base, with each edge of the base having length $x$ inches, as shown in the figure. The total length of all 12 edges of the box is 144 in. (a) Show that the volume of the box is given by the function $V(x)=2 x^{2}(18-x)$ (b) What is the domain of $V$ ? (Use the fact that length and volume must be positive) (c) Draw a graph of the function $V$ and use it to estimate the maximum volume for such a box.