/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 10 Find the circumference of the ci... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 10

Find the circumference of the circle with the given radius or diameter. $$r=0.563 \mathrm{m}$$

Short Answer

Expert verified
The circumference is approximately 3.5368 meters.

Step by step solution

01

Recall the Formula for Circumference

The circumference of a circle is calculated using the formula \( C = 2 \pi r \), where \( C \) is the circumference and \( r \) is the radius of the circle.
02

Substitute the Radius into the Formula

Insert the given radius \( r = 0.563 \mathrm{m} \) into the formula from Step 1. This gives us:\[ C = 2 \pi (0.563) \]
03

Calculate the Circumference

Calculate the value of \( C = 2 \pi (0.563) \). Using \( \pi \approx 3.14159 \), the calculation becomes:\[ C = 2 \times 3.14159 \times 0.563 \approx 3.5368 \mathrm{m} \]
04

Write the Final Answer

The calculated circumference of the circle, rounded to the nearest four decimal places, is approximately \( 3.5368 \mathrm{m} \).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

radius of a circle
The radius of a circle is a key concept in geometry. It's the distance from the center of the circle to any point on its edge. Understanding the radius is crucial because it acts as a building block for other calculations, like finding the circle's circumference or area. Here鈥檚 what is interesting about the radius:
  • It's always equal no matter where you measure from the center to the edge.
  • If you know the radius, you can calculate the diameter by doubling it (since the diameter is the distance across the circle passing through the center).
  • The radius is often given in problems because it's a straightforward measure that simplifies calculations.
For example, if a problem tells you the circle has a radius of 0.563 meters, like in our original exercise, you can directly use that value for further calculations.
circumference formula
When you need to find the distance around a circle, you use the circumference formula. The standard formula for circumference is:\[ C = 2 \pi r \] This formula tells us two things:
  • We need to multiply two times the product of \( \pi \) and the radius.
  • The formula demonstrates that circumference directly depends on the radius. A larger radius means a larger circle, thus more distance around it.
In the exercise, we use the given radius of 0.563 meters and substitute it into the formula, giving us \( C = 2 \pi (0.563) \). This step sets the stage for calculating the true circumference.
calculation with pi
\( \pi \), a fascinating number, is central to calculations involving circles. Representing the ratio of the circumference of any circle to its diameter, it's approximately equal to 3.14159, although it can go on forever as a non-repeating decimal. When calculating the circumference:
  • We use \( \pi \) to accurately scale the circle鈥檚 radius to find that circle's circumference.
  • Despite often being rounded to 3.14 or 22/7 in simpler computations, more precise problems will use a longer version such as 3.14159 or even more exact values depending on the needs.
This means when you perform the calculation \( C = 2 \pi (0.563) \), you multiply 2 with 3.14159 and then with 0.563, resulting in an approximate circumference of 3.5368 meters, as calculated in our example. This shows just how critical \( \pi \) is for precision in measurement.

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

\(\text {Solve the given problems.}\) The radius of a cylinder is twice as long as the radius of a cone, and the height of the cylinder is half as long as the height of the cone. What is the ratio of the volume of the cylinder to that of the cone?

Change the given angles to radian measure. $$60.0^{\circ}$$

Solve the given problems. What is the angle between the bisectors of the acute angles of a right triangle?

A person is in a plane \(11.5 \mathrm{km}\) above the shore of the Pacific Ocean. How far from the plane can the person see out on the Pacific? (The radius of Earth is \(6378 \mathrm{km}\).)

Solve the given problems. An observer is 550 m horizontally from the launch pad of a rocket. After the rocket has ascended \(750 \mathrm{m}\), how far is it from the observer?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.