पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४५६

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260 GANITA8ARABARGRAHA. multiplied with each other (as required by the rules bearing upon the finding out of areas whon the values of the sides are known). The area (so arrived at). when multiplied by the depth, gives rise to the oubical mensurb dosignated the kavympilotaka result. In the case 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 (eeparatoly) arrived at. The area values (so obtained) are added together and then divided by the number of (sectional) areas (taken into consideration). The quotient (so obtained) is multiplied by the value of the depth. This gives rise to (the oubical measure designated) the auld result. If one-third of the difference between these two results is added to the conditin rosult, it indeed becomes the accurate value (of the required cubical contents). Dramples in lasthation thereof. 12. There is a well whose (sectional) aroa happens to be an equilateral quadrilateral. The value (of each of the sides) of the top (sectional area) is 20 (hasld8), and that (of each of the sides) of the bottom (sectional area) is only 16 (asters). The depth is 9 (hosts. 0 you who know calculation, tell me quickly what the oubical measure here is 18. There is a well whose (sectional) area happens to be an equilateral triangular figure. The value (of each of the sides) of the top (sectional area) is 20 (hosta), and that (of each of tho sides) of the bottom (ecctional area) is 16; the depth is 9 (hastus). What is the value of the automatic cubical measure of 'the If u and b be the measures of a side of the top and bottom surfaces respectively of a truncated pyramid with a square baseit can be easily shown that the accurate measure of the cubical contents is equal to ३ है (@ + १२ + ob), where x is the height of the truncated pyramid. The formula given in the rule for the accurate measure of the cubical contents may be verified to be the same as his with the help of the following values for the Wormatika and Adro results given in the rule a + % + % x है, Bimilar vorifications may be arrived at in the case of broncated pyramid having an equilateral triangle or a rectangle for bhe base, and also in the case of runcated cone.