(Taken from http://Golf.about.com/od/historyofgolf/f/holesize.htm)
Like so many things in golf, the standardized size of the hole comes to us courtesy of the Royal and Ancient Golf Club of St. Andrews, with an assist from the links at Musselburgh.
In new rules issued in 1891, the R&A determined that the hole size should be standard on golf courses everywhere. So the R&A discussed just what exactly that size should be.
The size they decided on was 4.25 inches in diameter. The reason is that the folks at Musselburgh (now a 9-hole municipal course and called Royal Musselburgh Golf Club) had invented, in 1829, the first known hole-cutter. That ancient hole-cutter is still in existence and is on display at Royal Musselburgh.
That first hole-cutter utilized a cutting tool that was, you guessed it, 4.25 inches in diameter. The folks running the R&A apparently liked that size and so adopted it in their rules for 1891. And as was usually the case, the rest of the golf world followed in the footsteps of the R&A.
4.25 inches, at least 4 inches deep.
The circumference of a standard golf ball is about 144 millimeters or 5.2752 inches.
4.25 in. in diameter
The density of golfball is less then density of water
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Surface area of a sphere (the golfball) = 4*pi*radius2 square cm