Complete Question
The complete question is shown on the first uploaded image
Answer:
The gauge pressure that water has at the House A ![P_A = 257020.68 Pa](https://tex.z-dn.net/?f=P_A%20%3D%20257020.68%20Pa)
The gauge pressure that water has at the House B ![P_B = 188454 \ Pa](https://tex.z-dn.net/?f=P_B%20%3D%20188454%20%5C%20%20Pa)
Explanation:
From the question we are told that
The mass of water when full is ![m_f = 7.41* 10^{5} kg](https://tex.z-dn.net/?f=m_f%20%3D%207.41%2A%2010%5E%7B5%7D%20kg)
Generally the volume of water in this tank is mathematically represented as
![V = \frac{m }{\rho}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7Bm%20%7D%7B%5Crho%7D)
Where
is the density of water with a value of with a value of ![\rho = 1000 kg /m^3](https://tex.z-dn.net/?f=%5Crho%20%3D%201000%20kg%20%2Fm%5E3)
substituting values
![V = \frac{7.41 *10^5}{10^3}](https://tex.z-dn.net/?f=V%20%3D%20%20%5Cfrac%7B7.41%20%2A10%5E5%7D%7B10%5E3%7D)
![V = 741 m^3](https://tex.z-dn.net/?f=V%20%3D%20%20741%20m%5E3)
This volume is the volume of a sphere since the tank is spherical so
![V = \frac{4 \pi ^3}{3}](https://tex.z-dn.net/?f=V%20%3D%20%20%5Cfrac%7B4%20%5Cpi%20%5E3%7D%7B3%7D)
making r the subject of the formula
![r = 5.6134 m](https://tex.z-dn.net/?f=r%20%20%3D%205.6134%20m)
Now we can use this parameter to obtain the diameter
So
![d = 2 * r](https://tex.z-dn.net/?f=d%20%3D%202%20%2A%20r)
substituting values
![d = 2 * 5.6134](https://tex.z-dn.net/?f=d%20%3D%202%20%2A%205.6134)
![d = 11.23m](https://tex.z-dn.net/?f=d%20%3D%2011.23m)
The pressure the water has at faucet in House A is mathematically evaluated as
![P_A = \rho g h_A](https://tex.z-dn.net/?f=P_A%20%20%3D%20%5Crho%20g%20h_A)
This height is obtained as follows
![h_A = d+ 15](https://tex.z-dn.net/?f=h_A%20%3D%20%20d%2B%2015)
The value 15 is gotten from the diagram
so
![h_A = 15 + 11.23](https://tex.z-dn.net/?f=h_A%20%3D%20%2015%20%2B%2011.23)
![h_A = 26.22 m](https://tex.z-dn.net/?f=h_A%20%3D%20%2026.22%20m)
Now substituting values
![P_A = 26.23 * 9.8 * 1000](https://tex.z-dn.net/?f=P_A%20%3D%2026.23%20%2A%209.8%20%2A%201000)
![P_A = 257020.68 Pa](https://tex.z-dn.net/?f=P_A%20%3D%20257020.68%20Pa)
The pressure the water has at faucet in House B is mathematically evaluated as
![P_B = \rho g h_B](https://tex.z-dn.net/?f=P_B%20%20%3D%20%5Crho%20g%20h_B)
This height is obtained as follows
![h_B = d+ 15](https://tex.z-dn.net/?f=h_B%20%3D%20%20d%2B%2015)
The value 15 is gotten from the diagram
so
![h_B = d + 15 -h](https://tex.z-dn.net/?f=h_B%20%3D%20d%20%2B%2015%20-h)
substituting values
![h_B =11.23 + 15 -7](https://tex.z-dn.net/?f=h_B%20%3D11.23%20%2B%2015%20-7)
![h_A = 19.23 m](https://tex.z-dn.net/?f=h_A%20%3D%20%2019.23%20m)
Now substituting values
![P_B = 19.23 * 9.8 * 1000](https://tex.z-dn.net/?f=P_B%20%3D%2019.23%20%2A%209.8%20%2A%201000)
![P_B = 188454 \ Pa](https://tex.z-dn.net/?f=P_B%20%3D%20188454%20%5C%20%20Pa)