User:Donika Juthani/sandbox

CALCULATION OF MASS BY CHANGING VARIABLES IN TRIPPLE INTEGRALS ABSTRACT In this article, I shall discuss the use of calculus to find the mass of a dome. Integration can be used to determine the amount of materials necessory to construct a curved dome as well as calculate weight of that dome and determine the type of support structure required. INTRODUCTION Architects use simple geometry when the buildings are made out with ideal shapes such as squares,triangles,and simple polygons. But generally, most of the buildings are invloved with different other shapes such as curved domes, conical edges, ellipsoids,cylinders etc.

Calculus plays a major role in this kind of scenarios. Integral calculus is used to find the exact mass of a dome. When an architect wants to find the heat building losses based on temperature during a whole day, they graph time vs heat graph and calculate the area under the curve.

A dome is a 3D structure, just like a shell rather than a complete solid. The dome is divided into pieces which have constant densities.

The surface is divided into n smaller pieces firstly, S1,S2,S3,...Sn.