132k views
2 votes
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.

User Tanemaki
by
7.9k points

1 Answer

7 votes

Answer:

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

User Adam Nofsinger
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories