Extra Credit points$]$

$(1)$ Do the arrow shooting experiment $($by modifying either Python code or MATLAB code

provided on Brightspace$)$ on the ellipse

$\frac{x^2}{4}+\frac{y^2}{9}=1$

to calculate the area of the ellipse. Use the fact the area of the ellipse is

area $=ab$ for $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1.$ Try different trial numbers $n=1000,100,000,100,000,0000.$

$(2)$ Do the arrow shooting experiment on the cube to calculate the volume of the sphere with

radius $1.$ You need to submit your numerical codes with your solutions.