Spacial Reasoning and Calculus


Nnadozie Okarazu

Recently, Mr. Acha’s A.P Calculus AB class has begun a section dedicated to volume of solids caused by revolutions around axises. The idea behind this concept comes from understanding the area of a figure and the idea of a limit. Let’s take the area of a cylinder for example; its area is πr^2h. From the principles of definite integration, we know that a definite integral is equal to the limit as n (number of rectangles) approaches infinity of the summation, from i = 1 to n, of the area of rectangles (this idea would later be known as the Riemann Sums): f(xi)*delta x. Looking at the rectangles from a three-dimensional view and rotating them form a solid object. In addition, understanding that a cylinder is actually the augmentation of the the area of circles further helps to understand this topic. In essence, the volume of the solid object formed which is a definite integral, is equal to the limit as n approaches infinity of the summation, from i=1 to n of the area of a cylinder: πf(x)^2*delta x. In order to decipher this concept, the idea of spacial reasoning must be put into effect. Therefore, drawing and constructing figures that render in a three-dimensional space will be of benefit. For those who have yet to reach claculus, studying and in-depth analysis will be your best friend if you decide to use it–and use it wisely!
Practice make perfect!