Chapter 1: Q45. (page 19)

Estimate the number of jelly beans in the jar of Fig. 1–18.
FIGURE 1-18 Problem 45. Estimate the number of jelly beans in the jar.

Short Answer

Expert verified

There are 400 jelly beans in the jar.

Step by step solution

Step 1. Formula for the number of jelly beans

The expression for estimating the number of jelly beans in the jar is:

$N = \frac{V_{j}}{V_{b}}$

Here, $V_{j}$ is the volume of the jar and $V_{b}$ is the volume of the jelly bean.

Step 2. Calculation of the volume of the jelly bean

Let the length of the cylindrical jelly bean be approximately $h = 2.0 cm$ , and the radius be $r = 0.63 cm$ . Then, the volume of the jelly bean jar will be:

$\begin{array}{l} V_{b} = π r^{2} h \\ V_{b} = π {(0.63 cm)}^{3} (2.0 cm) \\ V_{b} = 2.49 {cm}^{3} \end{array}$

Suppose the volume of the jar is $V_{j} = 1110 {cm}^{3}$ . Due to the irregular shape of the jelly beans, they are not tightly packed. So, approximately 90% volume of the jar is filled.

The effective volume of the jar is:

$\begin{array}{l} V_{e, j} = 90 % (V) \\ V_{e, j} = (\frac{90}{100}) (1110 {cm}^{3}) \\ V_{e, j} = 999 {cm}^{3} \end{array}$

Step 3. Calculation of the number of jelly beans in the jar

The number of jelly beans in the jar can be calculated as:

$\begin{array}{l} N = \frac{V_{e, j}}{V_{b}} \\ N = \frac{999 {cm}^{3}}{2.49 {cm}^{3}} \\ N \approx 400 \end{array}$

Thus, there are 400 jelly beans in the jar.

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Estimate the number of jelly beans in the jar of Fig. 1–18.
FIGURE 1-18 Problem 45. Estimate the number of jelly beans in the jar.

Short Answer

Step by step solution

Step 1. Formula for the number of jelly beans

Step 2. Calculation of the volume of the jelly bean

Step 3. Calculation of the number of jelly beans in the jar

One App. One Place for Learning.

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Estimate the number of jelly beans in the jar of Fig. 1–18.FIGURE 1-18 Problem 45. Estimate the number of jelly beans in the jar.

Short Answer

Step by step solution

Step 1. Formula for the number of jelly beans

Step 2. Calculation of the volume of the jelly bean

Step 3. Calculation of the number of jelly beans in the jar

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Astrophysics

Linear Momentum

Famous Physicists

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Mechanics and Materials

Study anywhere. Anytime. Across all devices.

Estimate the number of jelly beans in the jar of Fig. 1–18.
FIGURE 1-18 Problem 45. Estimate the number of jelly beans in the jar.