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  • 解决涉及圆圈的问题

    In This Lesson
    ::在本课程中

    You will  apply  the formulas learned in This text will either use 3.14 to approximate or leave answers in terms of π .  First, you'll review π  and some of the rules for exponents. 
    ::您将应用此文本中学习的公式, 将使用 3. 14 来估计 或给出答案 。 首先, 您将审查 和一些 Expent 规则 。

     

    Have Some Pi
    ::吃点派

    You may not be familiar with leaving answers in terms of pi or even using the  π  button on  a calculator. In the first interactive question below, sort each number below into one of the two columns:  In Terms of Pi and Numerical Approximation . Each number has a pair, so put equivalent numbers in the same row. Round answers to the nearest hundredth.
    ::您可能不熟悉在计算器上留下 pi 或甚至使用 按钮的答案。 在下面第一个互动问题中, 将下面的每个数字排序为两列中的一栏: 皮和数字相近。 每个数字都有一对, 因此将相等的数字放在同一行中。 圆对最接近的百次 。

     

    Progress
    0 / 4
    1.

    Drag the values below to match them with their corresponding numerical approximation.
    ::拖动下方的值,使其与相应的数字近似值相匹配。

     

    @$\begin{align*}3.14\end{align*}@$
    ::@$\ begin{ 调整} 3. 14\ end{ 调整} $

    @$\begin{align*}6.28\end{align*}@$
    ::@ $\ begin{ aliign\\\\\ 6.28\ end{ aliign\\ $

    @$\begin{align*}12.56\end{align*}@$
    ::@$\ begin{ align\\\\ 12. 56\ end{ leign\\ $

    @$\begin{align*}1 \pi\end{align*}@$
    ::@ $\ begin{ aliign\\\\\\\\\\ pi\ end{ leign\\\\ $

    @$\begin{align*}2 \pi\end{align*}@$
    ::@ $\ begin{ aliign\\\\\ 2\ pi\ end{ leign} $

    @$\begin{align*}4 \pi\end{align*}@$
    ::@ $\ begin{ aliign} @ 4\ pi\ end{ aliign} $

    Numerical Approximations
    Terms of Pi

     

    Discussion Question
    ::讨论问题

    When checking an answer to see whether or not a specific number of square units is reasonable, would it be easier or harder to check the answer in terms of pi? How would you do so?
    ::当检查一个答案以确定具体数量的平方单位是否合理时,用 pi 来检查答案是否比较容易或困难? 你会怎么做呢?

    Use the Formulas
    ::使用公式

    Use 3.14 for  π  to determine the area and of the circles in the interactive. Repeat several times until you are comfortable with the two formulas. Remember the 3.14 is an estimation of π ,  but it does enable you to get a numerical answer, and not one in terms of π .  Record your work and answers for each circle you work with.
    ::用于 ° 的 3. 14 用于 确定 和 互动 中 的 区域 和 圆圈 。 重复 几次 , 直到 您对 两种公式 感到满意 。 记住 3. 14 是 ° 的估计值, 但是它确实 使您能够获得一个数字答案, 而不是 ° 。 记录您的工作和 圆圈的答案 。

     

     

     

     

    In this interactive, you practiced working with the formulas for exploring the dimensions of a circle. Now, you will apply them to real world situations and solve for the radius or diameter .
    ::在此互动中, 您练习使用公式来探索圆的维度。 现在, 您将把它们应用到现实世界中, 并解决半径或直径 。

     

    Room for Pi?
    ::Pi的房间?

    Ed and Sherry are putting a pool in their backyard. They want the pool to be a circle and the space they have for it is a 400 ft 2 square . What is the largest diameter the pool could be? 
    ::Ed和Sherry在他们的后院放一个游泳池。他们希望游泳池是一个圆圈,空间是400平方英尺。该游泳池的最大直径是多少?

    • Use the interactive and adjust the red dot to make the pool its maximum size. 
      ::使用互动点并调整红点,使集合体达到最大尺寸。
    • Determine the radius and diameter of the pool.
      ::确定池的半径和直径。

     

     

     

     

       Summary
    ::摘要

    • 3.14 is commonly  used as an approximation of  π .  
      ::3.14通常用作______的近似值。
    • For an exact solution , leave your answer in terms of  π  when solving for dimensions of a circle.
      ::对于确切的解决方案,在解析圆的维度时,请用 来回答答案。

    To evaluate the dimensions of a circle, d etermine what information you need and apply the appropriate formula:
    ::为评估圆的维度,确定需要哪些信息,并应用适当的公式:

    • The area is equal to pi multiplied by the square of the radius:  a = π ⋅ r 2

      ::区域等于 pi 乘以半径的平方: ar2
    • The perimeter of a circle (called the circumference) is equal to pi times the diameter:  C = π ⋅ d
      ::圆周(称为环绕)的周界等于直径的倍数:Cd