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7.6 Moments, Centers of Mass, and Centroids
464
____ 16. Find the volume of the solid generated by rotating the circle about
the y-axis.
a.
b.
c.
d.
e.
____ 17. Find the volume of the solid generated by rotating the circle about
the x-axis.
a.
b.
c.
d.
e.
____ 18.
Use the Theorem of Pappus to find the volume of the solid formed by revolving the
region bounded by the graphs of
about the x-axis. Round your answer to two
decimal places.
a.
1809.56
b.
2787.64
c.
2094.40
d.
3141.59
e.
3619.11
465 Chapter 7: Applications of Integration
7.6 Moments, Centers of Mass, and Centroids
Answer Section
7.7 Fluid Pressure and Fluid Force
466
7.7 Fluid Pressure and Fluid Force
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. The area of the top side of a piece of sheet metal is 9 square feet. The sheet metal is
submerged horizontally in 8 feet of water. Find the fluid force on the top side. Round your answer to
one decimal place.
4,492.8 lb
4,420.8 lb
4,348.8 lb
4,622.4 lb
4,838.4 lb
____ 2. Find the buoyant force of a rectangular solid of the given dimensions submerged in water so
that the top side is parallel to the surface of the water. The buoyant force is the difference between
the fluid forces on the top and bottom sides of the solid. Round your answer to two decimal places.
561.60 lb
748.80 lb
2,246.40 lb
249.60 lb
187.20 lb
467
Chapter 7: Applications of Integration
____
3.
Find the fluid force on the vertical side of the tank, where the dimensions are given in
feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.
a.
b.
c.
d.
e.
____ 4. Find the fluid force on the vertical side of the tank, where the dimensions are given in feet.
Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.
a.
b.
c.
d.
e.
7.7 Fluid Pressure and Fluid Force
468
____ 5.
Find the fluid force on the vertical side of the tank, where the dimensions are given in
feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.
a.
b.
c.
d.
e.
____ 6. Find the fluid force of a square vertical plate submerged in water, where meters
and the weight-density of water is 9800 newtons per cubic meter.
a.
b.
c.
d.
e.
469 Chapter 7: Applications of Integration
____ 7. Find the fluid force of a triangular vertical plate submerged in water, where the
dimensions are given in meters and the weight-density of water is 9800
newtons per cubic meter.
a.
b.
c.
d.
e.
____ 8. The figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per
cubic foot. Dimensions in the figure are in feet. Determine force on this part of the concrete form
a.
b.
c.
d.
e.
7.7 Fluid Pressure and Fluid Force
470
____ 9.
The figure is the vertical side of a form for poured concrete that weighs 140.7 pounds
per cubic foot. Dimensions in the figure are in feet. Determine force on this part of the concrete form.
a.
b.
c.
d.
e.
____ 10. A cylindrical gasoline tank is placed so that the axis of the cylinder is horizontal. Find the
fluid force on a circular end of the tank if the tank is half full, assuming that the diameter is
feet and the gasoline weighs 42 pounds per cubic foot.
a.
b.
c.
d.
e.
____ 11.
A cylindrical gasoline tank is placed so that the axis of the cylinder is horizontal.
Find the fluid force on a circular end of the tank if the tank is full, assuming that the diameter is
feet and the gasoline weighs
pounds per cubic foot. (Evaluate one integral by a geometric formula
and the other by observing that the integrand is an odd function.) Round your answer to two
decimal places.
a.
b.
c.
d.
e.
471 Chapter 7: Applications of Integration
____ 12.
A circular plate of radius r feet is submerged vertically in a tank of fluid that weighs
w pounds per cubic foot. The center of the circle is
feet below the surface of the fluid. The
fluid force on the surface of the plate is given by
Find the fluid force on the circular
plate as shown in the figure given
feet and
feet. Round your answer to one decimal
place.
a.
b.
c.
d.
e.
7.7 Fluid Pressure and Fluid Force
472
____ 13.
A rectangular plate of height h feet and base b feet is submerged vertically in a tank
of fluid that weighs w pounds per cubic foot. The center of the plate is k feet below the surface of the
fluid. The fluid force on the surface of the plate is given by
Find the fluid force on the
rectangular plate as shown in the figure given
feet and
feet. Round your answer to one
decimal place.
a.
b.
c.
d.
e.
____
14.
A porthole on a vertical side of a submarine (submerged in seawater) is square
. Find the fluid force on the porthole, assuming that the center of the square is
feet below the
surface.
a.
b.
c.
d.
e.
____
15.
The vertical cross section of an irrigation canal is modeled by
where x is measured in feet and
corresponds to the center of the canal. Use the integration
capabilities of a graphing utility to approximate the fluid force against a vertical gate used to stop
the flow of water if the water is feet deep. Round your answer to three decimal places.
a.
b.
c.
d.
e.
473 Chapter 7: Applications of Integration
7.7 Fluid Pressure and Fluid Force
Answer Section
