Chapter 1, Problem 9CCSR

Solution

The volume of the fourth gift box to the nearest cubic inch.

  $\left(\text{D}\right)410\text{ in}{\text{.}}^3$

Given:

The different sizes gift boxes made by the company are

  

Concept Used:

• If there is the strict inequality symbol $<\text{ or}>$, then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$, then use a bracket $\left[\right]$ on the interval
• To graph the endpoint with strict inequality $<\text{ or}>$, use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$, use the bracket or a solid circle at that endpoint.
• Multiplying or dividing an inequality by a negative number reverse the inequality sign.
• Volume of cuboid: $V=\text{Length}\times \text{Width}\times \text{Height}$

Calculation:

Note that the length of the square base of the gift box is 1.5 times the length of the previous figure and the height of the box is same for each figure as 9 inches.

So, the length of the square base of the fourth figure should be $4.5\times 1.5=6.75$ inches.

Thus, the volume of the fourth gift box is

  $\begin{array}{l}V=6.75\times 6.75\times 9\\ =410.06\\ \approx 410\text{ in}{\text{.}}^3\end{array}$

Thus, the volume of the fourth gift box is about $410\text{ in}{\text{.}}^3$ .