Explanation Given information: The water level is raising at a rate only 0.05 min/ft when the water is 12 ft deep. Calculation: The water flow into the tank at a rate of 80 f t 3 / min . Let A is the rate of water flowing out from the tank, r is the radius of tank, and y is the height of tank, Then the volume of water present in tank, V = 1 3 π r 2 y .................. ( 1 ) and tan ( θ ) = r y = 20 40 ⇒ r = y 2 . Where, d V d t = ( 80 − A ) f t 3 / min Differentiate equation (1) with respect to time from both sides. V = 1 3 π r 2 y .................. ( 1 ) d V d t = d d t ( 1 3 π r 2 y ) d V d t = d d t ( 1 3 π ( y 2 ) 2 y ) [ ∵ r = y 2 ] d V d t = 1 3 × 4 π d d t ( y 3 ) d V d t = ( 3 y 2 ) 3 × 4 π d y d t d V d t = y 2 π 4 d y d t Substitute d V d t = ( 80 − A ) f t 3 / min and when y = 12 and d y d t = 0

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Differential Equations

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Chapter 3.7, Problem 48PS

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To find the rate of water flowing out from the tank.

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Chapter 3.7, Problem 47PS

Chapter 3.7, Problem 49PS

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Chapter 3 Solutions

Calculus

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To find the rate of water flowing out from the tank.

Solution Summary: The author calculates the rate of water flowing out of the tank at 2.25ft3/mathrmmin.

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To find the rate of water flowing out from the tank.

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Chapter 3 Solutions