Open in App
Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Chapter 20: Chapter 20

Problem 378

Next question

The circumference of a tree trunk is \(6.6 \mathrm{ft}\). a) What is the diameter of the trunk? b) What is the area of a cross-section of the tree trunk?

Short Answer

Expert verified
a) The diameter of the tree trunk is approximately \(2.1 \mathrm{ft}\). b) The area of a cross-section of the tree trunk is approximately \(3.463 \mathrm{ft}^2\).
See the step by step solution

Step by step solution

Unlock all solutions

Get unlimited access to millions of textbook solutions with Vaia Premium

Try Premium for free

Over 22 million students worldwide already upgrade their learning with Vaia!

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: a) Finding the Diameter of the Trunk

Given the circumference of the tree trunk, we can determine the diameter using the formula: Circumference = \(\pi d\) Here, circumference = \(6.6 \mathrm{ft}\) and \(\pi\) is approximately equal to \(3.14159\). So, \(6.6 = 3.14159d\). Now, we need to find the value for d (diameter) by dividing the circumference by \(\pi\). d = \(\frac{6.6}{3.14159}\) d = \(2.1 \mathrm{ft}\) The diameter of the tree trunk is approximately \(2.1 \mathrm{ft}\).

Step 2: b) Finding the Area of a Cross-section of the Tree Trunk

To find the area of a cross-section of the tree trunk, we need to use the formula: Area = \(\pi r^2\) First, we need to determine the radius (r) of the tree trunk. The radius is half the diameter; thus, let's divide the diameter by 2. r = \(\frac{2.1}{2}\) r = \(1.05 \mathrm{ft}\) Now, we can plug the value of r into the formula: Area = \(3.14159 (1.05) ^ 2\) Area = \(\approx 3.463 \mathrm{ft}^2\) The area of a cross-section of the tree trunk is approximately \(3.463 \mathrm{ft}^2\).

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Access millions of textbook solutions in one place

  • Access over 3 million high quality textbook solutions
  • Access our popular flashcard, quiz, mock-exam and notes features
  • Access our smart AI features to upgrade your learning
Get Vaia Premium now
Access millions of textbook solutions in one place

Most popular questions from this chapter

Chapter 20

The ratio of the areas of two circles is \(9: 4\). The length of the radius of the larger circle is how many times greater than the length of the radius of the smaller circle?
Chapter 20

Find the area of a circle whose radius is 7 in. [Use \(\pi=22 / 7]\).
Chapter 20

In a circle whose radius is 12, find the area of a minor segment whose arc has a central angle of \(60^{\circ}\). [Leave the answer in terms of \(\pi\), and in radical form.]
Chapter 20

The area of circle 0 is 36 sq. in. If there are \(40^{\circ}\) contained in central angle \(\mathrm{COD}\), find the number of square inches In the area of sector COD.
Chapter 20

The ratio of the area of two circles is \(16: 1\). If the diameter of the smaller circle is 3 , find the diameter of the larger circle.
See all solutions

More chapters from the book ‘Geometry’

See all chapters

Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

  • Flashcards & Quizzes
  • AI Study Assistant
  • Smart Note-Taking
  • Mock-Exams
  • Study Planner
Join over 22 million students in learning with our Vaia App
Create your free account now
Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Math

Pure Maths

Read Explanation
Math

Geometry

Read Explanation
Math

Calculus

Read Explanation
Math

Decision Maths

Read Explanation
Math

Mechanics Maths

Read Explanation
Math

Statistics

Read Explanation
View all explanations