Question

1. The lateral surface area S of a cone excluding its base is given by where r is the radius of the base and h is the height. Determine the radius of a cone which has a lateral surface area 1200 m2 and a height of 20 m, by using the fixed point iteration with Start withr 17, and perform calculations in Matlab until two consec utive iterates do not differ by more than 10-8. What do you observe re garding the order of convergences

Answer 1

% Observations The radius of the cone with the given precision is 15. 2041cm The given function gives the iteration values which are convergent With the given precision Iterations are stopped at 20: The code is written such that at the end of each iteration the new value of r is displayed and the error between two succsessive iterations is also displayed x0-17 maxiter=50; tol=1e-08; X-zeros (1,50) x(1)=x0; for i=1 : maxiter X ( i+1)=1 200/ (pi *sqrt (X (1) ^2+2 0"2 ) ) ; err-abs (x(i+1)-X (1) ) ; if (abs (err) iter=1 ; radius-17error"2 . 448 iter-2 radius-14.552error-0.89136 iter-3radius-15.4433error-0.3268 iter-4;radius-15.1165error-0.11963 iter-5:radius-15.2362error-0.043821 iter-6;radius-15.1923error-0.016048 iter=7: radíu3=15. 2084error=0.0058778 iter=8; radius=15. 2025er-or=0.0021527 iter=9, radius=15. 2047error=0.00078844 iter-10:radius-15.2039error 0.00028877 iter=11, radius=15. 2042error=0.00010576 iter-12:radius-15.2041error-3.8735e-05 iter=13, radius-:15. 2041error=1.4187e-05 iter=14, radius=15. 2041error=5.1959e-06 iter=15 ; radíu3=15 . 204 1error=1 . 903e-06 iter-16;radius-15.2041error-6.9697e-07 iter=17: radius=15. 2041error=2.5527e-07 iter-18:radius-15.2041error-9.3492e-08 iter-19:radius-15.2041error-3.4241e-08 iter-20:radius-15.2041error-1.2541e-08