IM 8.5.20 Lesson: The Volume of a Sphere

Here is a method for quickly sketching a sphere:
[list][*]Draw a circle.[/*][*]Draw an oval in the middle whose edges touch the sphere.[/*][/list][img]data:image/png;base64,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[/img]
Practice sketching some spheres. Sketch a few different sizes. For each sketch, draw a radius and label it r.
[size=150]Here are a cone, a sphere, and a cylinder that all have the same radii and heights. The radius of the cylinder is 5 units. When necessary, express all answers to the following questions in terms of [math]\pi[/math].[/size][br][img]data:image/png;base64,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[/img][br][br]What is the height of the cylinder?
What is the volume of the cylinder?
What is the volume of the cone?
What is the volume of the sphere? Explain your reasoning.
[size=150]Here are a cone, a sphere, and a cylinder that all have the same radii and heights. Let the radius of the cylinder be [math]r[/math] units. When necessary, express answers in terms of [math]\pi[/math].[/size][br][img]data:image/png;base64,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[/img][br] [br]What is the height of the cylinder in terms of [math]r[/math]?
What is the volume of the cylinder in terms of [math]r[/math]?
What is the volume of the cone in terms of [math]r[/math]?
What is the volume of the sphere in terms of [math]r[/math]?
A volume of the cone is [math]\frac{1}{3}[/math] the volume of a cylinder. The volume of the sphere is what fraction of the volume of the cylinder?
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Information: IM 8.5.20 Lesson: The Volume of a Sphere