provide matlab code for thw whole problem

Problem $6[28$ marks$].$ A wedge is cut out of a circular cylinder of radius $5$ by two planes. One plane is

perpendicular to the axis of the cylinder. The other intersects the first at an angle of $45$ along a

diameter of the cylinder. See graph below,

a$.[4$ marks$]$ Find the volume of the wedge.

b$.[8$ marks$]$ Compute the optimum number of sub$-$intervals $n_{905}$ and width $h_{\text{g}\text{o}\text{p}\text{t}}$ so that the integral in

part a can be evaluated using the composite trapezoidal rule and composite Simpson's $\frac{1}{3}-$ rule.

c$.[12$ marks$]$ Write a program in MATLAB which first computes the optimum value of $n,n_{\text{a}\text{p}\text{t}},$ in the

composite trapezoidal rule and composite Simpson's $\frac{1}{3}-$ rule and then evaluate the value of the

integral with $n=n_{\text{a}\text{p}\text{t}}+2.$

d$.[4$ marks$]$ Compute the relative errors and use MATLAB function timeit to measure the execution

time of the algorithms with different $n$ in part $c.$ Provide the meaningful comments on the obtained

results.