Question

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

Answer 1

Answer:

cylinder

Step-by-step explanation:

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. What did he find?  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:

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