/*! 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 48 A circular rug is 6 feet in diam... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 48

A circular rug is 6 feet in diameter. How many feet of fringe is required to edge this rug?

Short Answer

Expert verified
The circular rug will require approximately 18.85 feet of fringe to edge it.

Step by step solution

01

Understand and note down given details

The diameter of the rug, \(d\), is given as 6 feet.
02

Use the Circumference formula

Apply the formula for the circumference of a circle, \(C = \pi d\). Here, \(\pi\) is roughly 3.14159, and \(d\) (the diameter of the rug) is 6 feet.
03

Compute the circumference

To find the length of the fringe which is the same as the rug's circumference, multiply \(\pi\) (3.14159) by the diameter (6 feet): \(C = \pi \times 6\) feet.

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.

Circle Circumference
The circumference of a circle is an important geometric concept that represents the complete distance around the circle. It's like measuring the perimeter of a polygon, but in this case, we're dealing with a smooth-edged circle. To find the circumference, we use the mathematical formula:
  • \( C = \, \pi \, d \)
  • \( C = \, 2 \pi \, r \)
Both formulas will give you the circumference, depending on whether you have the diameter \( d \) or the radius \( r \), which is half the diameter.Using \( \pi \approx 3.14159 \), you can precisely calculate how much of the material, like fringe, is needed to encircle the circular rug or any other round object.
Diameter Calculation
Understanding diameter is crucial for solving many circular problems. The diameter of a circle is a straight line passing through the center, connecting two points on its boundary. It's like slicing a pizza down the middle to make sure both halves are the same size. The diameter \( d \) is twice the radius \( r \):
  • \( d = 2r \)
  • Conversely, \( r = \frac{d}{2} \)
In some exercises, you might have to calculate the diameter if only the circumference is given. For instance, if you know the circumference, you can rearrange the formula \( C = \pi d \) to find \( d \):\[ d = \frac{C}{\pi} \]Familiarity with these relationships makes it easier to tackle various geometry problems.
Mathematical Problem Solving
Problem-solving in mathematics often requires a clear approach and understanding of what's being asked. For problems involving circles, you should:
  • Identify what you know 鈥� in our example, we started with the diameter.
  • Determine what the question is asking 鈥� we needed to find the fringe length, which is the circumference.
  • Apply the appropriate formula and do the math step-by-step.
  • Take note of units 鈥� here, it's feet, consistent throughout the problem.
This methodical approach will help you not just with circles, but in all areas of math where you need to solve step-by-step, ensuring consistent results.
Mathematical Formula Application
Applying formulas is a powerful tool in mathematics that simplifies problems significantly. Once a geometric relationship is understood, like the circle's circumference and diameter connection, applying the formula becomes straightforward. Here鈥檚 how you do it:- With given diameter \( d = 6 \) feet, apply \( C = \pi d \)- Plug in the value: \( C = 3.14159 \times 6 \)- Calculate: \( C \approx 18.84954 \) feetThis calculated circumference is how many feet of material you'll need to fringe the rug. Correct formula application ensures that complex-sounding problems have simple solutions. Practice makes this process second nature!

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

In the musical Company, composer Stephen Sondheim describes the marriage between two of the play's characters as "parallel lines who meet." What is the composer saying about this relationship?

Two cylindrical cans of soup sell for the same price. One can has a diameter of 6 inches and a height of 5 inches. The other has a diameter of 5 inches and a height of 6 inches. Which can contains more soup and, therefore, is the better buy?

Can a triangle contain two right angles? Explain your answer.

How does elliptic geometry differ from Euclidean geometry?

Describe one way in which topology is different than Euclidean geometry.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.