1. You have a ball with a diameter of 14.5 inches. Write a MATLAB program (initializing all constant values) that finds the surface area of the ball (4r2 where r is the radius) and the volume of the ball (4/3r3).
2. The acceleration of an oscillating spring is: a = -A2cos(t), where A is the displacement (2.994 cm), is the angular frequency (0.788 radians per second) and t is the time in seconds. Find the acceleration for times ranging from 0 to 10 seconds (incrementing by ½) using the values defined above. The acceleration should be in meters per second squared (i.e. you must convert the displacement value and remember that 100 cm is equal to 1 m). Create a table that includes the time in the first column and the corresponding accelerations in the second column.
3. The volume of a package (in the shape of a bx) with a square base is: v = x2h where v is the volume, x is the length and width of the base of the package and h is the height of the package. Write a MATLAB program to find the volume a group of packages where the x value varies from 3 to 17.5 feet (in 6 inch increments) and where the height varies from 4 to 10 feet (8 inch increments). Your answer should be a two-dimensional matrix with all possible combinations.