EECE 200 Lab Report, Spring 2008

Modeling Data in Excel HACHEM Amira 200900208 Section 1 Tuesday, November, 25, 2008 In this report, I am going to represent a project about cones through Excel. It will show the effect of the radius of a cone on his volume and his area. Entering the data will be in a simple way, using Excel tools. This report is represented as following: - Introduction - Outline - Work Description: 1) Modeling Process: Definition & Useful equations of cones 2) Tools: Excel tools used to represent the model 3) Results: The chart - Conclusion - References 1) Definition & Useful equations of cones This part of report represents cones in math: definition, description, properties. In general, a cone is a pyramid with a circular cross section. A right cone is a cone with its vertex above the center of its base. It converges to his vertex (Fig 1). However, when used without qualification, the term "cone" often means "right cone." Fig .1 The cone A right cone of height "h" and base radius "r" oriented along the Z-axis, with vertex pointing up, and with the base located at Z=0 can be described by the parametric equations for and . The opening angle of a right cone is the vertex angle made by a cross section through the apex and center of the base. For a cone of height "h" and radius "r", it is given by The formula for the volume of a cone is: Since the base area is a circle, again we can substitute the area formula for a circle into the volume formula, in place of the base area. The final formula for the volume of a cone is: The total surface area "T" is given by the following formula: With "s" = slant height: 2) Excel Tools First, we have to enter the needed data in cells. We'll have a table where we can examine the volume and the area of the cone depending on his radius. The height of the cone is fixed (it is equal to 20 centimeter). The radius is variable. We don't have to enter each value every time: we can do it in a simpler way using relative and absolute addresses. Excel’s formula copying feature has an updating capability which will enter the appropriate formula into the cells below. This is the relative address feature of Excel. Absolute addresses are used for data in general and for design variables or parameters in particular. Excel updates all relative addresses and not just the one we are interested. To make the increment address fixed, we need to assign it an absolute address in the formula. Absolute addresses are defined by the use of a dollar sign preceding the address. To specify the absolute column, you would put $ in front of the letter corresponding to the column. To specify the absolute row, you would put $ in front of the number of the row. We should enter the following formulas of The volume: =(1/3)*pi()*B7*F7^2 The area: =pi()*F7*($B$7^2+F7^2)^0.5 We need to copy cells through the different columns of radius, volume and area. Second, we have to build a chart showing the evaluation of the volume and the area of the cone with the different values of radius. We should insert the chart, give it a title, name the three(3) different axis, and add a legend to differentiate the two (2) graphs. 3) The Chart At the end we'll have a chart with two (2) graphs and the table showing us the values of radius, volume and area (Fig.2). Conclusion: We notice that the volume and the area are increasing: they are directly proportional with the radius. The Excel gave us a simple way to notice these variability and relations. References: www.mathworld.wolfram.com www.math.com www.mathforum.org Appendices