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Deck 11: Section 6: Vectors and the Geometry of Space
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Question
Identify the following quadric surface. 
A) hyperboloid of two sheets
B) elliptic cone
C) ellipsoid
D) elliptic paraboloid
E) hyperboloid of one sheet
A) hyperboloid of two sheets
B) elliptic cone
C) ellipsoid
D) elliptic paraboloid
E) hyperboloid of one sheet
Question
Use the shell method to find the volume of the solid below the surface formed by revolving the curve 
about the z-axis and above the xy-plane.
A)
B)
C)
D)
E)
about the z-axis and above the xy-plane.A)
B)
C)
D)
E)
Question
Identify the following quadric surface. 
A) hyperboloid of one sheet
B) elliptic cone
C) hyperboloid of two sheets
D) elliptic paraboloid
E) ellipsoid
A) hyperboloid of one sheet
B) elliptic cone
C) hyperboloid of two sheets
D) elliptic paraboloid
E) ellipsoid
Question
The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve 
in the yz-plane about the z-axis. All measurements are in centimeters and the bushing is set on the xy-plane. Use the shell method to find its volume. Round your answer to one decimal place.
A)
B)
C)
D)
E)
in the yz-plane about the z-axis. All measurements are in centimeters and the bushing is set on the xy-plane. Use the shell method to find its volume. Round your answer to one decimal place.A)
B)
C)
D)
E)
Question
Identify the following quadric surface. 
A) Elliptic cone
B) Hyperboloid of two sheets
C) Elliptic paraboloid
D) ellipsoid
E) Hyperboloid of one sheet
A) Elliptic cone
B) Hyperboloid of two sheets
C) Elliptic paraboloid
D) ellipsoid
E) Hyperboloid of one sheet
Question
Find the length of the minor axis of the ellipse generated when the surface 
is intersected by the plane 
.
A)
B)
C)
D)
E)
is intersected by the plane .A)
B)
C)
D)
E)
Question
Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve
Coordinate Plane
Axis of Revolution
A)
B)
C)
D)
E)
Coordinate Plane
Axis of Revolution
A)
B)
C)
D)
E)
Question
Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve
Coordinate Plane
Axis of Revolution
A)
B)
C)
D)
E) none of the above
Coordinate Plane
Axis of Revolution
A)
B)
C)
D)
E) none of the above
Question
Given the equation of a surface of revolution 
find the equation of its generating curve in the yz-plane rotating about the y-axis.
A)
B)
C)
D)
E)
find the equation of its generating curve in the yz-plane rotating about the y-axis.A)
B)
C)
D)
E)
Question
Identify the following quadric surface. 
A) elliptic paraboloid
B) elliptic cone
C) hyperboloid of two sheets
D) hyperboloid of one sheet
E) ellipsoid
A) elliptic paraboloid
B) elliptic cone
C) hyperboloid of two sheets
D) hyperboloid of one sheet
E) ellipsoid
Question
The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve 
in the yz-plane about the z-axis. Find an equation for the surface of revolution.
A)
B)
C)
D)
E)
in the yz-plane about the z-axis. Find an equation for the surface of revolution.A)
B)
C)
D)
E)
Question
Identify the equation of the following graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Some planet is an oblate ellipsoid rather than a sphere because of the forces caused by its rotation. The equatorial radius of this planet is 4739 miles and the polar radius is 4394 miles. Find the equation of the ellipsoid. (Assume that the center of a planet is at the origin and that the trace formed by the plane 
corresponds to the equator.)
A)
B)
C)
D)
E)
corresponds to the equator.)A)
B)
C)
D)
E)
Question
Identify the following quadric surface. 
A) ellipsoid
B) elliptic cone
C) elliptic paraboloid
D) hyperboloid of one sheet
E) hyperboloid of two sheets
A) ellipsoid
B) elliptic cone
C) elliptic paraboloid
D) hyperboloid of one sheet
E) hyperboloid of two sheets
Question
Identify the following quadric surface. 
A) hyperboloid of one sheet
B) elliptic cone
C) elliptic paraboloid
D) hyperboloid of two sheets
E) hyperbolic paraboloid
A) hyperboloid of one sheet
B) elliptic cone
C) elliptic paraboloid
D) hyperboloid of two sheets
E) hyperbolic paraboloid
Question
The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve 
in the yz-plane about the z-axis. The bushing has a hole of 4 centimeters in diameter through its center and parallel to the axis of revolution. All measurements are in centimeters and the bushing is set on the xy-plane. Find the volume of the rubber bushing. Round your answer to two decimal places.
A)
B)
C)
D)
E)
in the yz-plane about the z-axis. The bushing has a hole of 4 centimeters in diameter through its center and parallel to the axis of revolution. All measurements are in centimeters and the bushing is set on the xy-plane. Find the volume of the rubber bushing. Round your answer to two decimal places.A)
B)
C)
D)
E)
Question
Find an equation for the surface of revolution generated by revolving the curve 
in the xz-plane about the z-axis.
A)
B)
C)
D)
E)
in the xz-plane about the z-axis.A)
B)
C)
D)
E)
Question
Identify the equation of the following graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the equation of the surface satisfying the conditions, and identify the surface. The set of points equidistant from the point (2, 4, 5 ) and the plane 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find an equation of a generating curve given the equation of its surface of revolution. 
Equation of Curve Coordinate Plane
Axis of Revolution
A)
xz-plane z-axis
B)
xz-plane z-axis
C)
yz-plane y-axis
D)
yz-plane z-axis
E)
yz-plane y-axis
Equation of Curve Coordinate PlaneAxis of Revolution
A)
xz-plane z-axisB)
xz-plane z-axisC)
yz-plane y-axisD)
yz-plane z-axisE)
yz-plane y-axis
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Deck 11: Section 6: Vectors and the Geometry of Space
1
Identify the following quadric surface.
A) hyperboloid of two sheets
B) elliptic cone
C) ellipsoid
D) elliptic paraboloid
E) hyperboloid of one sheet
A) hyperboloid of two sheets
B) elliptic cone
C) ellipsoid
D) elliptic paraboloid
E) hyperboloid of one sheet
hyperboloid of one sheet
2
Use the shell method to find the volume of the solid below the surface formed by revolving the curve about the z-axis and above the xy-plane.
A)
B)
C)
D)
E)
about the z-axis and above the xy-plane.A)
B)
C)
D)
E)
3
Identify the following quadric surface.
A) hyperboloid of one sheet
B) elliptic cone
C) hyperboloid of two sheets
D) elliptic paraboloid
E) ellipsoid
A) hyperboloid of one sheet
B) elliptic cone
C) hyperboloid of two sheets
D) elliptic paraboloid
E) ellipsoid
ellipsoid
4
The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve in the yz-plane about the z-axis. All measurements are in centimeters and the bushing is set on the xy-plane. Use the shell method to find its volume. Round your answer to one decimal place.
A)
B)
C)
D)
E)
in the yz-plane about the z-axis. All measurements are in centimeters and the bushing is set on the xy-plane. Use the shell method to find its volume. Round your answer to one decimal place.A)
B)
C)
D)
E)
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5
Identify the following quadric surface.
A) Elliptic cone
B) Hyperboloid of two sheets
C) Elliptic paraboloid
D) ellipsoid
E) Hyperboloid of one sheet
A) Elliptic cone
B) Hyperboloid of two sheets
C) Elliptic paraboloid
D) ellipsoid
E) Hyperboloid of one sheet
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Unlock for access to all 20 flashcards in this deck.
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6
Find the length of the minor axis of the ellipse generated when the surface is intersected by the plane .
A)
B)
C)
D)
E)
is intersected by the plane .A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
7
Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve
Coordinate Plane
Axis of Revolution
A)
B)
C)
D)
E)
Coordinate Plane
Axis of Revolution
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
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8
Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve
Coordinate Plane
Axis of Revolution
A)
B)
C)
D)
E) none of the above
Coordinate Plane
Axis of Revolution
A)
B)
C)
D)
E) none of the above
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
9
Given the equation of a surface of revolution find the equation of its generating curve in the yz-plane rotating about the y-axis.
A)
B)
C)
D)
E)
find the equation of its generating curve in the yz-plane rotating about the y-axis.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
10
Identify the following quadric surface.
A) elliptic paraboloid
B) elliptic cone
C) hyperboloid of two sheets
D) hyperboloid of one sheet
E) ellipsoid
A) elliptic paraboloid
B) elliptic cone
C) hyperboloid of two sheets
D) hyperboloid of one sheet
E) ellipsoid
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
11
The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve in the yz-plane about the z-axis. Find an equation for the surface of revolution.
A)
B)
C)
D)
E)
in the yz-plane about the z-axis. Find an equation for the surface of revolution.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
12
Identify the equation of the following graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
13
Some planet is an oblate ellipsoid rather than a sphere because of the forces caused by its rotation. The equatorial radius of this planet is 4739 miles and the polar radius is 4394 miles. Find the equation of the ellipsoid. (Assume that the center of a planet is at the origin and that the trace formed by the plane corresponds to the equator.)
A)
B)
C)
D)
E)
corresponds to the equator.)A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
14
Identify the following quadric surface.
A) ellipsoid
B) elliptic cone
C) elliptic paraboloid
D) hyperboloid of one sheet
E) hyperboloid of two sheets
A) ellipsoid
B) elliptic cone
C) elliptic paraboloid
D) hyperboloid of one sheet
E) hyperboloid of two sheets
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
15
Identify the following quadric surface.
A) hyperboloid of one sheet
B) elliptic cone
C) elliptic paraboloid
D) hyperboloid of two sheets
E) hyperbolic paraboloid
A) hyperboloid of one sheet
B) elliptic cone
C) elliptic paraboloid
D) hyperboloid of two sheets
E) hyperbolic paraboloid
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
16
The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve in the yz-plane about the z-axis. The bushing has a hole of 4 centimeters in diameter through its center and parallel to the axis of revolution. All measurements are in centimeters and the bushing is set on the xy-plane. Find the volume of the rubber bushing. Round your answer to two decimal places.
A)
B)
C)
D)
E)
in the yz-plane about the z-axis. The bushing has a hole of 4 centimeters in diameter through its center and parallel to the axis of revolution. All measurements are in centimeters and the bushing is set on the xy-plane. Find the volume of the rubber bushing. Round your answer to two decimal places.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
17
Find an equation for the surface of revolution generated by revolving the curve in the xz-plane about the z-axis.
A)
B)
C)
D)
E)
in the xz-plane about the z-axis.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
18
Identify the equation of the following graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
19
Find the equation of the surface satisfying the conditions, and identify the surface. The set of points equidistant from the point (2, 4, 5 ) and the plane .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
20
Find an equation of a generating curve given the equation of its surface of revolution. Equation of Curve Coordinate Plane
Axis of Revolution
A) xz-plane z-axis
B) xz-plane z-axis
C) yz-plane y-axis
D) yz-plane z-axis
E) yz-plane y-axis
Equation of Curve Coordinate PlaneAxis of Revolution
A)
xz-plane z-axisB)
xz-plane z-axisC)
yz-plane y-axisD)
yz-plane z-axisE)
yz-plane y-axis Unlock Deck
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Unlock Deck
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Unlock for access to all 20 flashcards in this deck.
