(related to Problem: The Ball Problem)

If a round ball is placed on the level ground, six similar balls may be placed round it (all on the ground), so that they shall all touch the central ball.

As for the second question, the ratio of the diameter of a circle to its circumference we call $\pi;$ and though we cannot express this ratio in exact numbers, we can get sufficiently near to it for all practical purposes. However, in this case, it is not necessary to know the value of $\pi$ at all. Because to find the area of the surface of a sphere we multiply the square of the diameter by $\pi$; to find the volume of a sphere we multiply the cube of the diameter by one-sixth of $\pi$. Therefore we may ignore $\pi$, and have merely to seek a number whose square shall equal one-sixth of its cube. This number is obviously $6.$ Therefore the ball was $6$ ft. in diameter, for the area of its surface will be $36$ times $\pi$ in square feet, and its volume also $36$ times $\pi$ in cubic feet.

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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