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Chapter 1: Problem 24

To ship figurines, the figurines are placed in a rectangular box and then small packing pellets are added. The base of the box has an area of \(4.4\) in. \(^2\), and the height of the box is \(6.5 \mathrm{in}\). If the volume of the air in the box after the figures and pellets are added is \(8.0 \mathrm{in}^3\), which of the following is closest to the combined volume of the figurines and pellets in the box? A) \(1.9\) in. \(^3\) B) \(20.6\) in \(^3\) C) \(28.6\) in \(^3\) D) \(117.84 \mathrm{in.}^3\)

Short Answer

Expert verified
The combined volume of the figurines and pellets in the box is approximately \(20.6 in^3\).

Step by step solution

01

Calculate the total volume of the box

Using the formula for the volume of a rectangular prism, we have: Volume = Base Area × Height. The base area of the box is \(4.4\) in.\(^2\), and the height of the box is \(6.5\) in. So, the total volume of the box is: \(V = 4.4 in^2 \times 6.5 in = 28.6 in^3\)
02

Calculate the volume of figurines and pellets

To find the combined volume of the figurines and pellets, we need to subtract the volume of the air from the total volume of the box: \(Combined\ volume = Total\ volume - Air\ volume = 28.6 in^3 - 8.0 in^3\)
03

Calculate the difference

Subtract 8.0 in\(^3\) from the total volume of 28.6 in\(^3\): \(28.6 in^3 - 8.0 in^3 = 20.6 in^3\)
04

Choose the closest answer

Now, we compare the combined volume we calculated to the given options. Option B is \(20.6 in^3\), which is the closest to our calculated volume of figurines and pellets. Therefore, option B is the correct answer.

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