MATLAB Lab $4($Function$)$

Note: For all labs and assignments copy and paste into a Word file your program $($script

file$),$ the relevant command window and plots if applicable. Try to condense the print$-$out

as best as possible.

Objective

Introduction to user defined functions in MATLAB.

Procedures

The objective of this exercise is to minimize the total surface area of a cylindrical metal can for a

given volume and compare that area to that of a sphere of equal volume. Assume that the volume

is equal to $$~~$3\mathrm{.}1416.$

For this exercise, first create two user function files:

cylinder.m Inputs $-$ radius, height Outputs $-$ volume, area

sphere.m Input $-$ radius Outputs $-$ volume, area

Next create a MATLAB program $($script $.$m file$)$ to perform the following steps:

For cylinder:

$(1)$ Display table headings for cylinder radius, height, volume and area

$(2)$ For radius values of $0\mathrm{.}5$ to $1$ in steps of $0\mathrm{.}05$

Compute the height resulting in constant volume

Call cylinder.m to calculate and return cylinder volume and area

Display the results formatted to $4$ significant figures

Find and display the minimum cylinder area and corresponding radius and height.

For sphere:

$(3)$ Calculate and display the sphere radius for a volume of $.$

$(4)$ Call sphere.m to calculate, return and display sphere volume and area.

Finally, compare the minimum cylinder area to the sphere's area.

A program template ENGR$1204\_$Lab$4\_$template.m is shown below and can be downloaded

from WebCampus.

Formulas

Cylinder: volume $=r^{2}h,$ area $=2rh+r^2+r^2=2r(r+h)$

$($sides$)($top$)($bottom$)$

Sphere: $,$ volume $=(\frac{4}{3})r^3,$ area $=4r^2$