Answer
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 onesixth of pi.
Therefore we may ignore pi,
and have merely to seek
a number whose square shall equal onesixth 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.
