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kozerog [31]
3 years ago
10

Archimedes calculated the volume of a sphere by comparing it to what solid? prism cylinder pyramid box

Mathematics
1 answer:
Stella [2.4K]3 years ago
3 0
<h2>Answer:</h2>

cylinder

<h2>Step-by-step explanation:</h2>

Archimedes was a brilliant mathematician. This man rose the formula of the volume of a sphere by comparing this shape to a cylinder. The volume of a sphere is hard to calculate by comparing this object to a cube. So Archimedes imagined cutting a sphere into two halves, called hemispheres.  So an hemisphere gave him a flat surface, which is easier to work with. Therefore, if he'd find the volume of a hemisphere, then he'd multiply the result by 2 and would get the volume of a sphere. Then he imagined a hemisphere within a cylinder as the one shown below. Also, he imagined a cone within the same cylinder. <em>What did he find?  </em>He found that the volume of the hemisphere should be equal to the volume of the cylinder minus the volume of the cone:

V=\pi r^3-\frac{1}{3}\pi r^3 \\ \\ V=\frac{2}{3} \pi r^3

Then the volume of a sphere is twice this volume:

\boxed{V=\frac{4}{3} \pi r^3}

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