Q5.A rectangular box (no top) is welded together using sheet metal. The length of the box's base is 18 in. longer than its width. The total surface area of the sheet metal that is used is 2,500 in a. Using polynomials derive an expression for the volume V in terms of x. Write a script file for the following: b. Make a plot of V versus x for ssx s3s in. c. Determine the dimensions of the box that maximizes the volume and determine that volume. Hint use conv, polyder, roots and polyval build-in functions). Q6. A cylinder has radius r and height h is drawn within a sphere such that it touches the surface of a sphere (see figure). The radius of the sphere is R- n a. Derive a polynomial expression for the volume V of the cylinder in terms of Ah. Write a script file for the following: b. Plot of V versus h for 0shs11inch. c. Using the roots command determine h if the volume of the cylinder is 2,000 inch d. Determine the value of h that will generate a the cylinder with the largest possible volume, and determine that volume. (Hint use polyder, roots and polyval build-in functions). Q3 pts Q5 pls 06 pts Q1 pts Script file 2 Script file 2 Script file 5 Seript file Q4 Q2 ans Script file 2 l. On time & followed5 Script file 2 Total 50