Question

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 22 feet and a height of 12 feet. Container B has a diameter of 18 feet and a height of 19 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.

Answer 1

a) 4561.59 ft^3

b) 17.93 ft

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:

`V = \pi (d^2)/(4)*h`

- The volume of water in container A of diameter ( da ) and height ( ha ):

`V_a = \pi (d_a^2)/(4)*h_a\\\\V_a= \pi (22^2)/(4)*12\\\\V_a = 4561.59253 ft^3`

- 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 ):

`V_b = V_a = 4561.59253 ft^3` .. Answer ( a )

- The volume of water contained in container also takes the shape of cylinder and can be expressed as:

`V_b = \pi (d_b^2)/(4)*h\\\\h= (4*V_b)/(\pi*d_b^2 )\\\\h = (4*4561.59253)/(\pi*18^2 ) \\\\ h = 17.926 ft`

Answer: The level of water in container B is h = 17.93 ft