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6 Nov 2021
Problem 5
Page 491
Section: Focus on Problem Solving
Chapter 6: Application of Integration
Textbook ExpertVerified Tutor
6 Nov 2021
Given information
To find:
The depth of the water decreases at a constant rate regardless of the shape of the bowl.
Step-by-step explanation
Step 1.
The rate of change of volume of water is given as
where $k$ is some positive constant and 
is the area of the surface when the water has depth 
.
is the area of the surface when the water has depth .The rate of change of the depth of water with respect to time is 
.
.By the Chain rule,
From equation (1),
The total volume of water up to a depth is
is
where 
is the area of cross section of the water at depth 
.
is the area of cross section of the water at depth .
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805