Problem 40
Page 474
Section 6.6: Applications to Physics and Engineering
Chapter 6: Application of Integration
Given information
The diameter of the gate is 4 m and the height of the gate below water surface is 10 m.
The dam is given by the figure as follows:
Step-by-step explanation
The radius of the gate is 2 m and the depth of the center of the gate from the surface of water is 10 m.
Let the angle made by a radius passing through a point 
, located on the circular edge of the gate with the horizontal be 
, then the depth of the point is given by 
. substitute 
into to obtain the depth of the point is 
.
The width of a horizontal strip of the gate passing through the point is 
.The length of an infinitesimal section of perimeter around the point making an angle 
with the center of the disc is 
.The height (thickness) of the horizontal strip of disc that corresponds to this small section of perimeter is 
.
Single Variable Calculus: Early Transcendentals
Solutions
Chapter
Section
- Problem 1
- Problem 2
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7a
- Problem 7b
- Problem 8
- Problem 9
- Problem 10
- Problem 11b
- Problem 11b
- Problem 12
- Problem 14
- Problem 15
- Problem 16
- Problem 17
- Problem 18
- Problem 19
- Problem 20
- Problem 21
- Problem 22
- Problem 23
- Problem 24
- Problem 25
- Problem 26
- Problem 28a
- Problem 28b
- Problem 29a
- Problem 29b
- Problem 29c
- Problem 30a
- Problem 30b
- Problem 30c
- Problem 31
- Problem 32
- Problem 33
- Problem 34
- Problem 35
- Problem 36
- Problem 37
- Problem 38
- Problem 39b
- Problem 39c
- Problem 39d
- Problem 40
- Problem 41
- Problem 42
- Problem 43
- Problem 44
- Problem 45
- Problem 46
- Problem 47
- Problem 48
- Problem 49
- Problem 50
- Problem 51a
- Problem 51b
- Problem 52a
- Problem 52b
- Problem 52c