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. 189.--THE YORKSHIRE ESTATES. The triangular piece of land that was not for sale contains exactly eleven acres. Of course it is not difficult to find the answer if we follow the eccentric and tricky tracks of intricate trigonometry; or I might say that the application of a well-known formula reduces the problem to finding one-quarter of the square root of (4 x 370 x 116) -(370 + 116 - 74) squared--that is a quarter of the square root of 1936, which is one-quarter of 44, or 11 acres. But all that the reader really requires to know is the Pythagorean law on which many puzzles have been built, that in any right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. I shall dispense with all "surds" and similar absurdities, notwithstanding the fact that the sides of our triangle are clearly incommensurate, since we cannot exactly extract the square roots of the three square areas. [Illustration: A |\ | \. | \ . |5 \ . | 7 \ . E +--------- +C . | | ` . . | | `. . |4 |4 ` . . | 7 | ` .. D----------+----------------- B F ] In the above diagram ABC represents our triangle. ADB is a right-angled triangle, AD measuring 9 and BD measuring 17, because the square of 9 added to the square of 17 equals 370, the known area of the square on AB. Also AEC is a right-angled triangle, and the square of 5 added to the square of 7 equals 74, the square estate on A C. Similarly, CFB is a right-angled triangle, for the square of 4 added to the square of 10 equals 116, the square estate on BC. Now, although the sides of our triangular estate are incommensurate, we have in this diagram all the exact figures that we need to discover the area with precision.