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The volume of a sphere whose radius is 9 meters is: 3,054 meters3

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โˆ™ 2010-05-24 10:10:47
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Q: What is the volume of a sphere whose radius is 9 meters?
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How can you prove that the volume of a sphere is equal to the volume of a cylinder provided their radii are equal and the height of the cylinder is equal to the diameter of the sphere?

I'm quite sure this is impossible to prove, because the volume of a sphere is not equal to the volume of a cylinder with the same radius and height equal to the sphere's diameter. This can be shown as: Volume of sphere = (4*pi*r3) / 3. Volume of cylinder = pi*r2*h. Here, the height, h, of the cylinder = d = 2r. So, the volume of the cylinder = pi*r2*2r = 2*pi*r3, which obviously does not equal the volume of the sphere. The volume of half a sphere (with radius r) is equal to the volume of a cylinder(whose height is equal to its radius, r) minus the volume of a cone with the same height and radius. Therefore, the volume of a sphere is just double that. If you follow the nearby link, you can see a nice demonstration of that.


What is the volume of a sphere whose diameter is 12 cm?

The volume of a sphere with a diameter of 12cm is about 904.8cm3

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