8.8 比较卷数-interactive

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  比较卷数

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  Volume
  ::量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量量

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  appears in more professions than you might expect. Anyone who owns a 3D printer, engineers, shipping specialists, doctors, and so many more all use volume. Anytime you go to a store and compare prices based on size, you are comparing based on volume. You can divide the price by the volume to determine the price per unit volume. If you have a strong understanding of volume, you will be able to apply it professionally in ways which you didn’t even realize while studying it in school.
  ::出现在比预期更多的专业中。 拥有3D打印机、工程师、航运专家、医生和更多的使用量的人。 每当你到商店,根据体积比较价格时,你就会根据体积进行比较。 你可以将价格按体积除以体积来决定单位体积的价格。 如果你对体积有强烈的了解,你就可以以在学校学习时甚至没有意识到的方式专业地应用。

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  Cylinder, Cones, and Spheres
  ::圆柱、锥体和球体

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  The lesson  discussed  the relationship between cylinders, cones, and spheres. Determine the volumes of the three shapes in the interactive below:
  ::课程讨论了圆柱体、锥体和球体之间的关系。确定以下互动的三种形状的体积:

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  Discussion Questions
  ::讨论问题 讨论问题

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  1. How did you find the volume of the cylinder , cone, and sphere ?
     ::你是怎么找到气瓶、锥体和球体的体积的?
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  2. Are there any tricks that you could have used in retrospect?
     ::有没有什么可以让你回想起来的把戏?
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  3. Would this have worked if the solids did not have the same general dimensions ?
     ::如果固体没有相同的一般尺寸,这样做会有效吗?
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  4. Which shape would be the best to solve for first?
     ::先解决哪个形状最好?
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  5. If the volume of a cone is 5π, what will the volume of a sphere and cylinder be that have the same dimensions?
     ::如果锥体的体积是5,那么球体和圆柱体的体积是多少?
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  6. If the volume of a cylinder is 48π, what will the volume of a cone and sphere be that have the same dimensions?
     ::如果圆柱体的体积是48,锥体和球体的体积将是什么?
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  7. If the volume of a sphere is 20π, what will the volume of a cone and cylinder be that have the same dimensions?
     ::如果球体的体积是20°,锥体和圆柱体的体积将是什么?

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  Dimensional Comparison
  ::度量比较

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  Use the interactive below to explore how the  radius affects the  volume of the shapes.
  ::使用下面的交互方式来探索半径如何影响形状的体积。

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  Melting
  ::熔融

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  Four ice figures are made in the shapes of a cube a cylinder, a cone, and a sphere. The figures have equal dimensions, see Activity 1. Which ice figure will melt first? Which figure will melt last?
  ::四个冰位以立方体、圆柱体、锥体和球体的形状制成。数字的尺寸相等,见活动1,哪个冰位首先会融化?哪个冰位最后会融化?

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   Summary
  ::摘要

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  • The volume of a cylinder  with radius  $\begin{align*}r\end{align*}$  and height  $\begin{align*}2r\end{align*}$  is twice the volume of a sphere with  the same radius and   $\begin{align*}\tfrac32 \end{align*}$  times the volume of a cone with the same radius and height.
    ::圆柱体的体积为圆柱体的两倍,圆柱体的体积为圆柱体的两倍,圆柱体的体积为圆锥体的32倍,圆锥体的体积为圆锥体的32倍,圆锥体的体积与圆锥体的半径和高度相同。