The Greek mathematician Archimedes first discovered the relationship between a sphere's diameter and its volume in the third century B.C. He realized that a similarly sized cone and sphere together take up exactly as much room as two similarly sized cylinders. With the volumes for cylinders and cones already known, he concluded that a sphere's volume equals four-thirds of its radius' cube. The sphere's diameter relates to its radius even more directly; its diameter equals twice its radius.
Multiply the sphere's volume by 0.75, which is the inverse of four-thirds. If the sphere has a volume of 10 cubic inches then start with this formula: 10 x 0.75 = 7.5.
Find the cube root of this answer: 7.5^1/3 = 1.96. This is the sphere's radius, measured in inches.
Multiply the result by two: 1.96 x 2 = 3.92. This is the sphere's diameter, measured in inches.
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