Question

An asteroid is particular mathematical curve: a hypocycloid with four cusps. It is formed 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 Figure1. 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

(o,t FGE (1-2%)35 χに 3 "X 2

2 NS at shoroes only sota tion xl

oS in