Q45. Estimate the number of jelly bea... [FREE SOLUTION]

91影视

Chapter 1: Q45. (page 19)

Estimate the number of jelly beans in the jar of Fig. 1鈥�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:

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

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:

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

Thus, there are 400 jelly beans in the jar.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Estimate the number of jelly beans in the jar of Fig. 1鈥�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

Famous Physicists

Translational Dynamics

Electricity

Magnetism

Classical Mechanics

Geometrical and Physical Optics

Study anywhere. Anytime. Across all devices.

91影视

Estimate the number of jelly beans in the jar of Fig. 1鈥�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

Famous Physicists

Translational Dynamics

Electricity

Magnetism

Classical Mechanics

Geometrical and Physical Optics

Study anywhere. Anytime. Across all devices.

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