. A tank holds 100 gallons of water. Its inlet is 7 inches
in diametre and fills the tank at 5 gallons/min. The
outlet of the tank is twice the diametre of the inlet.
How many minutes will it take to empty the tank
if the inlet is shut off, when the tank is full and the
outlet is opened? (Hint: Rate of filling or emptying
is directly proportional to the diametre)
Answers
Given : A tank holds 100 gallons of water. Its inlet is 7 inches in diameter and fills the tank at 5 gallons/min.
The outlet of the tank is twice the diameter of the inlet.
To Find : How many minutes will it take to empty the tank if the inlet is shut off, when the tank is full and the outlet is opened
(Hint: Rate of filling or emptying is directly proportional to the diameter)
Solution:
considering Hint as given fact
Rate of filling or emptying is directly proportional to the diameter
=> 5 gallons/min. ∝ 7 inches
=> 5 / k = 7 / (2 * 7)
=> k = 10 gallons/min
Hence rate of emptying is is 10 gallons/min
Tank = 100 gallon
Time taken = 100/10 = 10 mins
In Actual Rate of filling ∝ cross section Area hence ( diameter )²
Considering that
=> 5 gallons/min. ∝ 7²
=> 5 / k = 7² / (2 * 7)²
=> k = 20 gallons/min
Hence rate of emptying is is 20 gallons/min
Tank = 100 gallon
Time taken = 100/20 = 5 mins
learn More :
A balloon rises straight up at 10 ft/s. An observer is 40 ft away from ..
brainly.in/question/3185935
Find the rate of change of volume of a cone w.r.t. its radius, when the ...
brainly.in/question/5376336
A tree company charges a delivery fee for each tree purchased in ...
brainly.in/question/9824354