CHAPTER VIII-CLOUI.ANTroNS REGARDING EXCAVATIONS. 265 The rule for arriving at the 'alue of the cubioal contents of a spherically bounded space : 28. The half of the cube of half the diametex, multiplied by nine, gives the approximate value of the cubical contents of a sphere. This (approximate value), multiplied by nime and divided by te? on neglecting the remainder, gives rise to the accurate value of the cubical measure. An example in allustration hereof. 29]. In the case of a sphere measuring 16 in diameter, calcu. late and tell me what the approximate value of (its) cubioal mea ure is, nd also the accurate measure (thereof) IThe rule for arriving at the approximate value as well as the accurate value of the cubical contents of an excavation in the form of a triangular pyramid, (the height whereof is taken to be equal to the length of one of the sides of the equilateral triangle forming the base) 802The eube of half the square of the side (of the basal equilateral triangle) is multiplied by ten ; and the square root (of the resulting product is divided by nine. This gives rise to the approximately calculated value (required). (This approximate ) value, when multiplied by three and divided by the square root of 28%. The volume of a sphere as given here is (1) approximately () , and (2) accurately = The correct formula for the cubi. 10 cal contents of a sphere is A = 'and this becomes camparable with the above valueif 4 is taken to be 10. Both the Mss. read तनवमांश 10 दशगुणं, making it appear that the accurate value is of the approximate value ; but the text adopted is तद्दशमांशं नवगुणं which makes the accurate value of the approximate one. It is easy to see that this gives a more accorate 10 result in regard to the measure of the cubcal contents of a sphere bhan the other reading 30. Algebraically represented the approximate value of the cubical contents of a briangular pyramid according to the rule comes to * /5 18 20 and the accurate value becomes equal to * 2; where 12 12 5.8 84
