पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४५९

CHAPTER VIII-CALCULATIONS REGARDING EXCAVATIONS. 261 aundra cubical measure, and of the accurate cubical meisure here? 14. There is a well whoso (sectional) area happens to be regularly circular. The (diameter of the) top (sectional area) is 20 dandas, and that of the bottom (sectional arca) is only 16 dandas. The depth is 12 dandas. What may be the harmantika, the aundra, and the accurate cubical measures here? 15. In relation to (an excavation whose sectional area happens to be) a longish quadrilateral figure (t.e., oblong), the length at the top is 60 (hastas), the breadth is 12 (hastas); at the bottom, these are (respectively) half (of what they measure at the top). The depth 8 (hastas). What is the cubical measure here? 16 (Here is another well of the same kind), the lengths (of whose sectional areas) at the top, at the middle, and at the bottom are (respectively) 90, 80, and 70 (hastus), and the breadths are (respectively) 32, 16, and 10 hastas. This is 7 (hastas) in depth. (Find out the required cubical measure.) 17. In relation to (an excavation whose sectional area happens to be) a regular circle, the diameter at the mouth is 60 (hastas), in the middle 30 (hastas), and at the bottom 15 (hastas). The depth is 16 hastas. 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 hastas at the top, 60 hastas in the middle, and 50 hastas at the bottom. The depth is 9 hastas. 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) :- 19-20. The breadth (of the central mass) increased by the top-breadth of the surrounding ditch, and (then) multiplied by 19-20. These stanzas deal with the measurement of the cubic contents of a ditch dug round a central mass of earth of any shape. The central mass may be in section a square, a rectangle, an equilateral triangle, or a circle ;