पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४५९

CHAPTER VIII--CALCULATIONS REGARDING EXCAVATIONS. 268 22. The length of a longis quadrilateral is 120 (data8) and the breadth is 40. The ditch around is as big as 4 dz!as in breadth and 8 in depth. (Find out the cubical contents.) The rule for arriving at the value of the cubical contents of an excavation, when the depth of the excavation varies (at various points), and also for arriving, when the cubioal contents of an excavation are known, at the depth of digging necessary in the case of another (known) area (so that the cubical contents may be the same) 23). The sum of the deptibs ( measured in different places) is divided by the number of places; this gives rise to the (average) depth. This hultiplied by the top area . (of the excavation) gives rise to the (required) cubical contents of the excavation in the case where that area is trilateral, quadrilateral or circular. The cubical contents (of a given excavation), when divided by the (known) value of another area, gives rise to the depth (to which there should be digging, so that the resulting cubical contents may be the same). Bomple8 in &lastration thereof. 24]. In an equilateral quadrilateral field, the ground covered by which has an extent measured by 4 data8 (in length and breadhh), the excavations are (in depth) 1, 2, 3, and 4 dates (in four different cases). What is the measure of the average depth (of the excavations) { 25]. There is a well with an equilateral quadrilateral section, the sides whereof are 18 hosts in measure its depth is 4 hostes. With the water of this (well), another well measuring 9 hostes at each of the sides (of the section) is illed. What is the depth (of this other well) ? When the measures of the sides of the top (sectional area) and also of the bottom (sectional area) are known, and when the 22. For finding out the total length of the surrounding ditch when th central mass of earth is rectangular in section, the measures of the sides as increased by the width or half the width of the ditch are added together according as the Kas mantiko or the Andra result is required.