Jain Journal 2001 10

Author(s): Jain Bhawan Publication
Publisher: Jain Bhawan Publication

Page 23

JADHAV THE VOLUME OF A RIGHT CIRCULAR CYLINDER
right circular cylinder with diameter 'd' and height (or rather depth) 'h', Nemicandra gives the following rule in the first chapter 'Lokasāmānyadhikara' of the TLS.
vāso tiguno parihi väsa-caütthähadohu khetta-phalan/ khetta-phalam vehagunam khadaphalam hoi savvattha //
Translation: When the diameter (vyāsa) (of the base of a right circular cylinder) is multiplied by three, it gives the circumference (paridhi). When this (result) is multiplied by a quarter of the diameter, it gives the area (kṣetraphala) (of the base of the cylinder). The area multiplied by the height (vedha) (of the cylinder) becomes the volume (khātaphala) (of that cylinder) in all.
The first part of the above rule finds the circumference 'C' of the base of a right circular cylinder :
C - 3d
[1] The second part finds the area 'A' of the base of a right circular cylinder :
A C.
75
[2]
The third part gives the formula for finding the volume 'V of a right circular cylinder :
4
where л is equal to 3.
In this way, he knew the formula [4].
3. Discussion
2.
(TLS v. 17 p. 18)
V = A.h
[3]
Substituting the value of 'A' from the formula [2] and then that of 'C' from the one [1] in the one [3] we have
V=7(9)2h
For calculating the volume of a cylinder or prism, the general formula is:
Volume = (Area of base ) x (Height)
[5]
This formula [5], according to B.B. Datta2, was known to the authors of the Sulba-sutras. This seems to be his perception only.
[4]
B.B. Datta, (1932), The Science of the Sulba, University of Calcutta. Kolkata, Reprinted in 1991. p. 101. Cf. also: B.B. Datta, and A.N. Singh (1980), Hindi Geometry, Revised by K.S. Shukla. Indian Journal of History of Science: 15, 121-188, Kolkata, p. 173.