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A spherical tank is used to hold water as shown below. The volume of water in tank can be computed using the following equation: V = µh² (³R = h) where: V: water volume in m³, h: depth of water in tank in m, R: tank radius in m. R Given that R = 3 m, and the volume of water is 30 m³, estimate the depth of water (h) by using: (2-A) the graphical estimation method (by hand) (2-B) the Bi-section method. You are required to continue with the iterations until you reach an absolute error below 0.0001. (2-C) the Newton-Raphson method. You are required to continue with the iterations until you reach an absolute error below 0.0001. Afterwards, compare between all applied methods in terms of applicability, accuracy, and speed. Support your comments using findings above.

A spherical tank is used to hold water as shown below. The volume of water in tank can be computed using the following equation: V = µh² (³R = h) where: V: water volume in m³, h: depth of water in tank in m, R: tank radius in m. R Given that R = 3 m, and the volume of water is 30 m³, estimate the depth of water (h) by using: (2-A) the graphical estimation method (by hand) (2-B) the Bi-section method. You are required to continue with the iterations until you reach an absolute error below 0.0001. (2-C) the Newton-Raphson method. You are required to continue with the iterations until you reach an absolute error below 0.0001. Afterwards, compare between all applied methods in terms of applicability, accuracy, and speed. Support your comments using findings above.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 68E
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Activity 2: A spherical tank is used to hold water as shown below. The volume of water in tank can be computed using the following equation: - V = πh² (³R = h) where: V: water volume in m³, h: depth of water in tank in m, R: tank radius in m. R Given that R = 3 m, and the volume of water is 30 m³, estimate the depth of water (h) by using: (2-A) the graphical estimation method (by hand) (2-B) the Bi-section method. You are required to continue with the iterations until you reach an absolute error below 0.0001. (2-C) the Newton-Raphson method. You are required to continue with the iterations until you reach an absolute error below 0.0001. Afterwards, compare between all applied methods in terms of applicability, accuracy, and speed. Support your comments using findings above. (Hint: find the exact estimation analytically and use it as a benchmark)
Transcribed Image Text:Activity 2: A spherical tank is used to hold water as shown below. The volume of water in tank can be computed using the following equation: - V = πh² (³R = h) where: V: water volume in m³, h: depth of water in tank in m, R: tank radius in m. R Given that R = 3 m, and the volume of water is 30 m³, estimate the depth of water (h) by using: (2-A) the graphical estimation method (by hand) (2-B) the Bi-section method. You are required to continue with the iterations until you reach an absolute error below 0.0001. (2-C) the Newton-Raphson method. You are required to continue with the iterations until you reach an absolute error below 0.0001. Afterwards, compare between all applied methods in terms of applicability, accuracy, and speed. Support your comments using findings above. (Hint: find the exact estimation analytically and use it as a benchmark)
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