/*! 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 273 approximate the (a) circumferenc... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 273

approximate the (a) circumference and (b) area of each circle. If measurements are given in fractions, leave answers in fraction form. radius \(=18.6 \mathrm{m}\)

Short Answer

Expert verified
The approximate circumference is 116.86 m and the area is 1085.09 m^2.

Step by step solution

01

Use the formula for circumference

2 脳 3.14 脳 18.6 =116.86 m.
02

Use the formula for area

To find the area, use the formula: 饾憙饾惖=蟺 r^2 The radius, r, is given as 18.6 m. Substitute this value into the formula to get: 3.14 脳 (18.6)^2 =3.14 脳 345.96 =1085.09 m^2

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.

Circumference Formula
The circumference of a circle is the distance around the edge of the circle. To find the circumference, you can use the formula:
\[ C = 2 \times \text{蟺} \times r \]
Here, 蟺 (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
For example, if the radius is 18.6 meters, the circumference is computed as follows:
\( C = 2 \times 3.14 \times 18.6 \)
That works out to be around 116.86 meters. It鈥檚 just like measuring the distance around a circular track. This formula is very handy when you need to calculate how long something is when it wraps around a circle.
Area Formula
The area of a circle implies the amount of space enclosed within its boundary. The formula you鈥檒l use is:
\[ A = \text{蟺} r^2 \]
This formula involves squaring the radius first, then multiplying by 蟺 (pi).
Take the radius (18.6 meters) and substitute it in:
\( A = 3.14 \times (18.6)^2 \)
Squaring 18.6 gives you approximately 345.96, then you multiply by 3.14.
The area comes out to about 1085.09 square meters.
Think of it as finding out how many square tiles you鈥檇 need to cover the inside of a large circular floor.
Approximation in Mathematics
In mathematics, we often need to approximate values to make calculations more manageable. Pi (蟺) is one such value, commonly approximated as 3.14. However, 蟺 is actually an irrational number, which means its exact value continues indefinitely without repeating.
Approximations are particularly useful when:
  • Precision is not critical to the task
  • Simplifying complex operations
  • Performing mental math
For instance, approximating 蟺 as 3.14 instead of using more digits gives us results that are fairly accurate and easy to handle, especially in everyday situations. It鈥檚 like using a map: it might not show every little detail, but it鈥檚 good enough to guide you to your destination.

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 following exercises, find the unit rate. Round to two decimal places, if necessary. The pressroom at a printing plant prints 540,000 sections in 12 hours. How many sections are printed per hour?

In the following exercises, convert each decimal to a fraction or mixed number. $$14.125$$

Salary Increase Danny got a raise and now makes\(\$ 58,965.95\) a year. Round this number to the nearest: (a) dollar (b) thousand dollars (c) ten thousand dollars.

The average American produces about \(1,600\) pounds of paper trash per year \((365\) days. How many pounds of paper trash does the average American produce each day? (Round to the nearest tenth of a pound.)

In the following exercises, find the unit price. Round to the nearest cent. Soap bars at 4 for \(\$ 3.39\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

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.