Question

In order to successfully complete this project, you need to study the following topics in the course textbook: - Volume using Cross Sections (Section 6.1) Volume using -Arc Length (Section 6.3) - Areas of Surfaces of Revolution (Section 6.4) Shells (Section 6.2) General Comments about t This project is designed to be done in groups of 3. The project report is reflection of your investigation on the questions. This means your report should begin with an introductory paragraph in which you discuss the question or problem that you are examining. Give a brief description about how you approached your work. Make sure all mathematical ideas and concepts are communicated effectively and clearly. If tables, figures, and graphs are included in your report, make sure they are numbered. The main body of the report should include correct references to equation numbers, figures, and tables. Type all your equations and number them sequentially. Screen shot of equations from different resources are unacceptable. If any external reference is used, include them in the reference section of your report; otherwise, it is considered as plagiarism. Final delivery of your report (no pdf). Only one report can be Your entire work must be typed. Handwritten reports are not is through mCourses Dropbox. Only word document is submitted per group. You cannot have multiple submissions. Hence, edit your work before submission. Editing process includes typographical errors, grammar, spelling errors, and run-on sentences. Side Note: At the end of your report, include a section and clearly list every member's responsibilities and contributions. Team members get different grades based on their contribution on the project. Evaluation For evaluating quality of your work, followings are considered: Mathematics and Analysis (70%) Thoughtful approach to the questions Correct use of mathematical concepts and notations Correct and clear calculation -Presentation (20%) Organization of ideas in meaningful order Clarity in discussion Table of contents Page number Numbering equations Caption for graphs and figures -writing (10%) Spelling/Grammar An asteroid is particular mathematical curve: a hypocycloid with four cusps. It is fomed by rolling a circle (shown in black) inside a fixed circle (shown in blue) with four time the radius. The trajectory of an asteroid is shown in Figure 1 Figure 1: Trajectory of an asteroid If the radius of the fixed circle is a, then the equation of an asteroid is given by Equation of an asteroid that needs to considered for this project is a. Use a graphing tool to graph the asteroid formulated in equation 2. b. Find arc length of this asteroid. c. Revolve the asteroid in part a about the x-axis to obtain a solid shape. Use a graphing tool to graph the solid shape. d. Find surface area of the shape graphed in part c. e. Find volume of the shape graphed in part c. Create an appendix section where your programming code for part a and c are included. Comment your code clearly.

Answer 1

Equation of an asteroid that needs to considered for this project is x2/3y2/ = 1 a. Use a graphing tool to graph the asteroid formulated in equation 2. pip (2) tfl wa ce = 1 S V he soteroi a 0 sAm nhe 2lpamangA b. Find arc length of this asteroid. Difterentiadm \ with vespeit Eo x, me A anL4S, T d x3 +プ dx =45 4x - 4 .Revolve the asteraid in part a about the x-axis to obtain a solid shape. Use a graphing tool to graph the solid shape. hae d. Find surface area of the shape graphed in part c Sarydn Rimamn m-Rant Sufau avta n y dx 0.05 0.803491 1 0.1 0.15 0.608001 3.68 0.2 0.25 0.468422 0.3 0.35 0.357119 Uing Rremanm amid-Pnt 4 0.4 0.45 0.265193 0 5 0.55 0.188462 0.6 6 0.65 0.124722 0.7 0.75 0.072906 0.8 0.85 0,032904 0.9 0.95 0.006164 10 SUM 3.67866 e. Find volume of the shape graphed in part c. 2 dx 1--3> 2 5 3. sis 77