Mark Background: Consider a regular dodecahedron object which has 12 faces. The surface area SA and volume v of the object is given by: SA = 3a2 25 + 1075 15 + 715 V=- 4 Q3 1 : 290f45 where a represents the edge length of the dodecahedron. The following MATLAB code is provided for SA and v. SA = 3.*a. 2*sqrt(25+10. sqrt(5)); V = (15+7.+sqrt(5))./4. a.^3; ! (a) Create the function file named dode with outputs SA and V (in that order) and input a, which can be a vector. How many element-by-element operation (i.e. **/ .) are unnecessary in the above SA and V code? Number of unnecessary element-by-element operations = [2 marks] Notes + suite Me (b) Determine the SA and v for a = 10. As a check, SA - 185.8116 and V = 206.9042 for a = 3. Provide your answers to 4 decimal places as printed by MATLAB. Surface area [4dp] [2 marks] Volume [4dp] = [2 marks] Notes + . (c) Consider x = -5:0.1:5 and a = sin(cos(x/2)). Determine the maximum SA for these a values and the corresponding V and a. Provide your answer to 4 decimal places as printed by MATLAB. [6 marks] Maximum SA [4dp] = [2 marks) Corresponding V[4dp] = [2 marks] Corresponding a [4dp) = [2 marks] (d) Rewrite the function file written in part (a) so that it does not use any element-by-element operations but still works with vector inputs. Copy and paste your MATLAB code in the plain text box below. You can also upload your m-file below (optional). [6 marks) BI U X2 x? DE E ABC 123