You are designing a spherical tank to hold water for a small village. The volume of liquid it can hold can be computed as V = nh²(3h) where V = volume [m³], h = depth of water in tank [m], and R = the tank radius [m]. Use Newton Raphson method with 2 iterations to find the height (h=?) for storing 28 m³ of water with 11 m diameter-tank. Take 7 = 3.1416 and initial guess for h=R.
You are designing a spherical tank to hold water for a small village. The volume of liquid it can hold can be computed as V = nh²(3h) where V = volume [m³], h = depth of water in tank [m], and R = the tank radius [m]. Use Newton Raphson method with 2 iterations to find the height (h=?) for storing 28 m³ of water with 11 m diameter-tank. Take 7 = 3.1416 and initial guess for h=R.
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![You are designing a spherical tank to hold water for a small village. The volume of liquid it can hold can be computed as
\[ V = \pi h^2 \left( 3R - \frac{h}{3} \right) \]
where \( V = \) volume \([m^3]\), \( h = \) depth of water in tank \([m]\), and \( R = \) the tank radius \([m]\). Use Newton Raphson method with 2 iterations to find the height (\( h = ? \)) for storing \( 28 \, m^3 \) of water with \( 11 \, m \) diameter-tank. Take \( \pi = 3.1416 \) and initial guess for \( h = R \).
**Choices**
- 1.451
- 1.422
- 1.8863
- 1.7412
**Diagram Explanation:**
The diagram on the right shows a cross-section of a spherical tank with label markings:
- \( R \) denotes the radius of the sphere.
- \( h \) represents the depth of the water in the tank.
- The section filled with liquid is shaded to indicate volume \( V \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97234a29-7009-4d8e-8d71-9606bd71717d%2Fe07b02e5-75d9-43f2-a057-412c49bfd850%2F3jb01p_processed.png&w=3840&q=75)
Transcribed Image Text:You are designing a spherical tank to hold water for a small village. The volume of liquid it can hold can be computed as
\[ V = \pi h^2 \left( 3R - \frac{h}{3} \right) \]
where \( V = \) volume \([m^3]\), \( h = \) depth of water in tank \([m]\), and \( R = \) the tank radius \([m]\). Use Newton Raphson method with 2 iterations to find the height (\( h = ? \)) for storing \( 28 \, m^3 \) of water with \( 11 \, m \) diameter-tank. Take \( \pi = 3.1416 \) and initial guess for \( h = R \).
**Choices**
- 1.451
- 1.422
- 1.8863
- 1.7412
**Diagram Explanation:**
The diagram on the right shows a cross-section of a spherical tank with label markings:
- \( R \) denotes the radius of the sphere.
- \( h \) represents the depth of the water in the tank.
- The section filled with liquid is shaded to indicate volume \( V \).
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