Part II: The Answers
462
Answers
701–800
735.
14,726 ft·lb
Here’s a view of the tank and its cross-section:
Let n be the number of subintervals of length Δ x and let x i
* be a sample point in the ith
subinterval. Consider a horizontal slice of water that is Δx feet thick and is x i
* feet from
the bottom of the tank with a width of w i
*
. This slice has a volume of
V
w
x
i
i
= ( )
π
*
2
3
∆ ft
By similar triangles, you have
w
x
i
i
*
*
= 5
6
, so w
x
i
i
*
*
= 5
6
; therefore, the volume becomes
V
w
x
x
x
x
x
i
i
i
i
= ( )
= ( )
=
( )
π
π
π
*
*
*
2
2
2
3
5
6
25
36
∆
∆
∆ ft
The force on this slice of water is
F
x
x
i
i =
( )
(
)
62 5 25
36
2
.
*
π
∆ lb
The distance this slice must travel to exit the tank is 6 −
(
)
x i
* feet. Therefore, the total
work required is