Help me for this question An aluminum fuel tank has a cylind

Help me for this question

An aluminum fuel tank has a cylindrical middle section and a semi-spherical ends. The outside diameter is 10 in., and the length of the cylindrical section is 24 in. The wall-thickness of the cylindrical section is t, and the wall-thickness of the semi-spherical ends is 1.5t. Determine t if the tank weight is 42.27 lb. The specific weight of aluminum is 0.101 lb/in^3. Determine the dimensions (radius r and height and the volume of the cylinder with the largest volume that can be made inside of a sphere with a radius R of 14 in. Construct the state model for a system characterized by the differential equation y + 6y + 11y + 6y = u.

Solution

Answers :

Q9)

%start the script

P=conv ([11.5-5], con ([1.5-5]))*(4*pi/3);

P (4) =p (4) + (4*pi/3)*5^3;

q=conv ([1-5], [1-5])*-1;

q (3) =q (3) +5^2;

q= [0 q];

q=pi*24*q;

z=p+q;

z (4)=z(4)-42.27lb

a=roots (z);

y=imag (a) ==0&real (a)>0&real (a) <15

t=a (find(y));

Fprint (‘t=%f in.\ ’t)

The following matlab output is

Y=

0

0

1

T=0.364535 in.

Therefore the value of t is =0.364535 in.

Q10)

%clear the command window screen clc

% obtain the plot for the volume function

fPlot(‘3.14*x*(14^@-(x/2)^2)’,[0 28]))

%take the minimum value of negative function to find the maximum value of volume height at that point

[H, fmax]=fminbnd (‘-3.14*x.*(-(x/2)^2+(1$)^2’,14,17)

%label the graph on x and y axes

X label (‘h’)

Ylabel (‘volume’)

R=sqrt (-(h/2) ^2+(14)^2

Fprint (‘the cylinder height h is %3.4f in. and radius r is %3.4f in,’h,r)

Fprintf (‘\ the largest volume of the cylinder is % f in ^3\\in^3\ ’,-fmax)

Output:

H=

16.1658

Fmax=-6.6327e+03

R=

11.4310

The largest volume of the cylinder is 6632.723061 in^3