in matlab create the following: You are designing a spherical tank to hold water

Question

in matlab create the following:

You are designing a spherical tank to hold water. The total volume of liquid contained in the tank can be computed as V = pi h^2 (3R - h)/3 where V is the volume (m^3), h is the depth of water in the tank (m), and R is the radius of the tank (m). If R = 3 m, to what depth must the tank be filled so that it holds 30 m^3? Use 3 iterations of the false-position method to determine your answer. Use initial guesses of 0 and R, and determine the relative error after each iteration.

Explanation / Answer

Solution:-

Given

A spherical tank to hold the water &

Volume of the liquid contained in the tank can be computed as

v = pi*h^2* (3R-h)/3 ----- Equation 1

Here V = Volume in cubic meter

h = depth of water in the tank which is meter, and

R = Radius of tank in meters

If R =3 m and V = 30 m3

then from Equation 1, we get as follows:-

30 = pi*h^2 (3*3-h)/3

30 = 3.14*3/3.14 = h^2(9-h)

So 28.7 = 9h^2- h^3

So by iteration method, for h = 2, result = " 28.7" ;

Hence h = 2

Relative error, for h = 2 then result "=28";

Henec Relative error= 28.7 - 28 = 0.7

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