A water tower has the geometry shown in the figure (the lower part is a cylinder

Question

A water tower has the geometry shown in the figure (the lower part is a cylinder with radius R and height h, and the upper part is a half sphere with radius R). Determine the radius R if h = 10 m and the volume is 1, 050 m^3. (Write an equation for the volume in terms of the radius and the height. Solve the equation for the radius, and use the double command to obtain a numerical value. Consider the following set of seven equations from a loop mesh circuit, with I representing current. Define a symbolic variable for each of the equations, and use MATLAB symbolic capability to solve for each unknown current. 3I_1 + 4I_2 + 2I_3 - I_4 + I_5 + 7I_6 + I_7 = 42 2I_1 - 2I_2 + 3I_3 - 4I_4 + 5I_5 + 2I_6 + 8I_7 = 32 I_1 + 2I_2 +3I_3 + I_4 +2I_5 +4I_6 + 6I_7 = 12 5I_1 + 10I_2 + 4I_3 +3I_4 + 9I_5 - 2I_6 + I_7 = -5 3I_1 + 2I_2 - 2I_3 - 4I_4 - 5I_5 - 6I_6 + 7I_7 = 10 -2I_1 + 9I_2 + I_3 + 3I-4 - 3I_5 + 5I_6 + I_7 = 18 I_1 - 2I_2 - 8I_3 + 4I_4 + 2I_5 + 4I_6 + 5I_7 = 17

Explanation / Answer

2)

a =

3 4 2 -1 1 7 1
2 -2 3 -4 5 2 8
1 2 3 1 2 4 6
5 10 4 3 9 -2 1
3 2 -2 4 -5 -6 7
-2 9 1 3 -3 5 1
1 -2 8 4 2 4 5

>> b

b =

42
32
12
-5
10
18
17

>> I=inv(a)*b

I =

4.9071
3.1358
9.4513
-9.8068
-7.9313
-0.9051
0.2928

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