/*! 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 5 If the diameter of a circle is \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 5

If the diameter of a circle is \(10 \mathrm{ft}\), what is the radius?

Short Answer

Expert verified
The radius of the circle is 5 ft.

Step by step solution

01

Understand the relationship between diameter and radius

The diameter of a circle is twice the length of its radius. Mathematically, this relationship can be expressed as: \[ d = 2r \] where \( d \) is the diameter and \( r \) is the radius.
02

Identify the given value

In the problem, the given value is the diameter of the circle, which is \(10 \text{ ft} \).
03

Rearrange the formula to solve for the radius

To find the radius, rearrange the formula \( d = 2r \) to solve for \( r \). Divide both sides by 2: \[ r = \frac{d}{2} \]
04

Substitute the given diameter into the formula

Substitute the given diameter value of \( 10 \text{ ft} \) into the formula: \[ r = \frac{10}{2} \]
05

Compute the radius

Calculate the value: \[ r = 5 \text{ ft} \]

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.

diameter and radius relationship
The relationship between the diameter and radius of a circle is fundamental in circle geometry. If you know one, you can always find the other. The diameter is simply twice the radius. This straightforward relationship is expressed by the formula:

\( d = 2r \)
where \( d \) stands for diameter and \( r \) stands for radius.

Conversely, if you have the diameter and need to find the radius, you just need to divide the diameter by 2. Mathematically, you rearrange the original formula to solve for \( r \):
\( r = \frac{d}{2} \)
This simple relationship helps in many geometric calculations and is essential for understanding circle properties.
basic algebra
Basic algebra is crucial when working with formulas in geometry. When faced with an equation like \( d = 2r \), you can rearrange it to solve for any variable. If given the diameter, you can find the radius by isolating \( r \).

Here鈥檚 how you do it step-by-step:
  • Start with the original equation:\
circle geometry
Understanding circle geometry involves knowing key properties and relationships within a circle. Two of the most important measurements are the diameter and the radius.

Some core properties of these measurements include:
  • The diameter is the longest straight line that passes through the center of the circle, touching the circumference at two points.

  • The radius is half of the diameter and extends from the center of the circle to any point on the circumference.

These properties help in solving various geometric problems, such as finding the area \( A \) or circumference \( C \) of a circle:
  • The area is given by \( A = \pi r^2 \)

  • The circumference is \( C = 2 \pi r \).

So, understanding the diameter and radius relationship is not just about solving simple equations; it is about forming the foundation for broader geometric calculations.鈥�

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

Evaluate the function for the given values of \(x\). \(t(x)=\left\\{\begin{aligned} x & \text { for } 0

Refer to the functions \(f\) and \(g\) and evaluate the functions for the given values of \(x\). \(f=\\{(2,4),(6,-1),(4,-2),(0,3),(-1,6)\\} \quad\) and \(\quad g=\\{(4,3),(0,6),(5,7),(6,0)\\}\) $$(g \circ f)(2)$$

A cell phone plan charges \(\$ 49.95\) per month plus \(\$ 14.02\) in taxes, plus \(\$ 0.40\) per minute for calls beyond the 600 -min monthly limit. Write a piecewise-defined function to model the monthly cost \(C(x)\) (in \$) as a function of the number of minutes used \(x\) for the month.

A function is given. (See Examples \(4-5)\) a. Find \(f(x+h)\). b. Find \(\frac{f(x+h)-f(x)}{h}\). $$f(x)=x^{2}-3 x$$

Determine if the function is even, odd, or neither. $$ m(x)=-4 x^{5}+2 x^{3}+x $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.