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260
GANITASĀRABANGRAHA.
multiplied with each other (as required by the rules bearing upon the finding out of areas when the values of the sides are known). The area (so arrived at), when multiplied by the depth, gives rise to the cubical measure designated the karmäntika result. In the Oase of those same figures representing the top sectional area and the bottom sectional area, the value of the area of each of) these figures is (aeparately) arrived at. The area values (80 obtained) are added together and thon divided by the number of (seotional) areas (taken into consideration). The quotient (80 obtained) is multiplied by the value of the depth. This gives rise to the oubical measure designated) the aundra result. If one-third of the difference between these two results is added to the karmāntika result, it indeed becomos the accurate value (of the required cubical contents).
Examples in illustration thereof. 124. There is a well whose (sectional) arca happens to be an equilateral quadrilatoral. The value (of each of the sides) of the top (sectional area) is 20 (hastas), and that (of each of the sides) of the bottom (sectional area) is only 16 (hastas). The depth is 9 (hastas). O you who know oalculation, tell me quickly what the oubical measure here is..
131. There is a well wboso (sectional) area happens to be an equilateral triangular figure. The value (of each of the sides) of the top (sectional area) is 20 (hastas), and that (of each of the sides) of the bottom (sectional area) is 16; the depth is 9 (hastas). What is the value of the karmantika cubical measure, of the
If a and be the measures of a side of the top and bottom surfaops respectively of
truncated pyramid with a squaro baso, it can be ossily shown that the acourate measure of the cubivel ountonte is equal to sha' + b + ab), where is the buight of the truncated pyramid. The formula given in the rule for the scourate measure of the cubical oontents may be verified to be the same as this with the help of the following values for tho Karmantika and Aundra results given in the rule:
K= (*+b)xhi A=4'11" xh. Bimilar vorifications may be arrived at in the case of tranoated pyramida aaving an equilateral triangle or rectangle for the base, and also in the one of tranoated cones..
