Respuesta :
Answer:
a) 4561.59 ft^3
b) 17.93 ft
Step-by-step explanation:
Given:-
- Container A and B are of cylindrical shape
- The diameter of container A, da = 22 ft
- The height of container A, ha = 12 ft
- The diameter of container B, db = 18 ft
- The height of container B, hb = 19 ft
- Container A is initially full while container B is empty.
- Water is pumped from container A to container B until container A is empty.
Find:-
a) The volume of water in container B
b) The level of water in container B
Solution:-
- The cylinder is initially full to the top. The volume of the water in container A takes the shape of container A. The volume of a cylindrical container is mathematically expressed as function of diameter and height, as follows:
[tex]V = \pi \frac{d^2}{4}*h[/tex]
- The volume of water in container A of diameter ( da ) and height ( ha ):
[tex]V_a = \pi \frac{d_a^2}{4}*h_a\\\\V_a= \pi \frac{22^2}{4}*12\\\\V_a = 4561.59253 ft^3[/tex]
- We are given that the water is pumped from the container A to B until all the water ( Volume ) is emptied from container A:
- The total amount of water available in container A, is V_a is all pumped into container B. Therefore, after the process of pumping container B will have the volume of water equivalent to the volume of water in container A before the pumping process started ( assuming no loss of water ):
[tex]V_b = V_a = 4561.59253 ft^3[/tex] .. Answer ( a )
- The volume of water contained in container also takes the shape of cylinder and can be expressed as:
[tex]V_b = \pi \frac{d_b^2}{4}*h\\\\h= \frac{4*V_b}{\pi*d_b^2 }\\\\h = \frac{4*4561.59253}{\pi*18^2 } \\\\ h = 17.926 ft[/tex]
Answer: The level of water in container B is h = 17.93 ft
