Mathematics in Ancient and Medieval India c6.s9.89

c6.s9.89

( i ) *The volume of solid bodies*. Āryabhaṭa I's formula for the volume of a sphere and that of a triangular pyramid are not quite correct.¹ His formula for a sphere is √(π).³ or 1.47 ³, the correct value being 4/3³ or 1.33. .³. The correct value was given by Bhāskara II.² The formula for that of the triangular pyramid is given incorrectly by Āryabhaṭa I ( *Gaṇita-pāda*, verse 8 ) as ½ × area of the triangular base × height. The correct formula for a square pyramid is given by Bhāskara II as ⅓ × radius × square base. For volume of the sphere, Bhāskar II has divided it into as many pyramids as there are unit square areas on the surface, its height being equal to the radius. Hence the volume of the sphere becomes equal to ⅓ of the sphere i.e. 4/3³.