पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४५७

CHAPTER VII-CALCULATIONS REGARDING EXCAVATIONS. 261 unda cubical measure, and of the accurate cubical measure here 14] . 'Thero is a well whose (sectiomal) area happens to bo regularly cironlar. The (diameter of the) top (sectional area} is 20 damdca, and that of the bottom (sectional area) is only 16 dddds. The depth is 12 datalsWhat may be the k«rnitka, the add. and the accurate cubical measures here ? 5. In relation to (an excavation whose sectional area happens to be) a longish quadrilateral figure (e.e.; oblong), the length at the top is 60 (hosts, the breadth is 12 (lostgth); at the bottom, these , are (respectively) half (of what they measure at the top). The depth is 8 (hexts. What is the cubical measure here ? 16]. (Here is another well of the same kind), the lengths (of whose sectional areas) at the topat the middle, and at the bottom are (respectively) 90, 80, and 70 (lastus), and the breadths are (respectively) 32, 16and 10 hrstsThis is 7 (hostas) in depth. (Find out the required cubical measure.) 17. In relation to (an excavation whose sectional area happens to ba) a regular circle, the diameter at the mouth is 60 (lastus), in the middle 80 (httas), and at the bottom 15 (hstas). The depth i8 16 hast8. . What is the calculated result giving its cubical measure 18]. In relation to (an excavation whose sectional area happens to be) a triangle, each of the three sides measures 80 lasts at the top, 60 hosts in the middle, and 50 hosters at the bottom. The depth is 9 hists. What is the calculated result giving its cubical contents ? The rule for arriving at the value of the cubical contents of a ditch, as also for arriving at the value of the cubical contents of an excavation having in the middle (of it) a tapering pro jection (of solid earth ) 199–20. The breadth (of the central mass) increased by the top-breadth of the surrounding ditch, and (Chen) multiplied by ५ 198–208. These stanzas deal with the measurement of the cubio contents of a ditoh dug round a central mass of earth of any shape. The central mass may be in section a squarea rectangle, an equilateral triangleor a circle;