# Notes--Obj 8

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```					            Objective 8:

The student will demonstrate an
understanding of the concepts and uses
of measurement and similarity.
Look at the cylinder shown below. Which
equation best represents the volume, V, of this
cylinder in terms of π?

A    V = 16πr2
B    V = 8πr2
C    V = 4πr2
D    V = 4πr3

Correct Answer - D        10-April 2006 #31
A triangular prism is shown below. What is the
volume of this triangular prism?

A     192 in.3
B     240 in.3
C     384 in.3
D     480 in.3

Correct Answer - A     10-April 2004 #27
Henry built a wooden storage shed in the shape of a rectangular
prism for his tools. If Henry plans to paint only the top, front,
left, and right sides of his shed, which is closest to the surface area
that will be painted?

A       121 ft2
B       181 ft2
C       154 ft2
D       91 ft2

Correct Answer - A                    11-April 2006 #27
A cube-shaped piece of playground equipment has a
cylindrical portion removed, as shown in the diagram.
The diameter of the opening is 5 feet. What is the
approximate volume of the remaining portion of the cube?
F     255 ft3
G     122 ft3
H     98 ft3
J     28 ft3

Correct Answer - H            11-Fall 2005 #46
A company plans to design a
new version of its Millennium
Doll that will be larger than the
old version. The figure below
shows the dimensions of the box
for the old version of the doll. If
all the dimensions of the box are
increased by 2 inches for the
new doll, what will be the total
surface area of the new box?
F      496 in.2
G      696 in.2
H      992 in.2
J      1920 in.2
Correct Answer - H   11-July 2004 #30
The figure shows a CD in its rectangular storage
case. Which is closest to the area of the storage
case not occupied by the CD?
A    55 cm2
B    46 cm2
C    51 cm2
D    60 cm2

Correct Answer - A        11-April 2006 #35
The drama department at McHenry High School has built
a stage floor in the shape of a regular octagon. The length
of each side of the octagon is 4 yards. CD is the apothem.
What is the approximate area of the stage floor?

F     57.9 yd2
G     76.8 yd2
H     115.9 yd2
J     154.5 yd2

Correct Answer - G                11-July 2006 #6
The figure shows a triangle on top of a rectangle. If
the area of the triangle is 83 square feet, which of the
following best represent the area of the rectangle?

A     405 ft.2
B     239 ft.2
C     322 ft.2
D     166 ft.2

Correct Answer - C          11-Fall 2005 #43
When the door handle is pushed down to open the door, it
makes a 45° angle with its former position. What is the
approximate arc length of the path traveled by the outside
end of the door handle when the handle is pushed down?
A      34.56 in.
B     11.88 in.
C     4.32 in.
D     2.16 in.

11-July 2006 #45
Correct Answer - C               Fall 2005 #15
The shaded area in the circle below represents the
section of a park used by the chamber of
commerce for a fund-raising event. What is the
approximate area of the section of the park used
for the fund-raiser?

A    339 square feet
B    1,357 square feet
C    4,071 square feet
D    12,214 square feet
Correct Answer - C            July 2004 #4
Mr. Krueger attended an event at the Good
Time Sports Arena. The arena is in the shape
of a circle with a radius of 200 feet. He parked
his car in the lot at point S, which is 250 feet
away from the entrance at point F. Mr.
Krueger left the arena through the exit at
point D and walked a straight-line path to
his parked car. About how far away
was his parked car from the exit
at point D?
F      200 ft
G      403 ft
H      492 ft
J      650 ft

Correct Answer - G                11-February 2006 #16
What is the area of the square in the figure?
A 5.2 square units
B    6.7 square units
C    27 square units
D    45 square units

Correct Answer - D           11-July 2004 #41
Which set of dimensions
corresponds to a
rectangular prism similar
to the one shown?

F 2 units by 3 units by 4 units
G 4 units by 2 units by 8 units
H 2 units by 1 unit by 6 units
J 4 units by 3 units by 6 units

Correct Answer - J   11-April 2004 #6
Which statement best describes why pentagon PQRST is similar
to pentagon VWXYZ?

A The ratio of the length of PT
to YZ equals the ratio of the
length of RS to WV.
B Both pentagons have
corresponding right angles.
C Pentagon VWXYZ is the
result of a translation of
pentagon PQRST.
D The ratio of the
corresponding sides of pentagons
PQRST and VWXYZ is 2:1.

Correct Answer - D                11-July 2004 #9
Use the
information in
each diagram
to find the pair of
similar polygons.

Correct Answer - B   Spring 2003 #13
Trapezoid KMPR is similar to trapezoid LNQS. Which
is closest to the perimeter of trapezoid LNQS?

A    23 units
B    31 units
C    25 units
D    63 units
Correct Answer - A      10-April 2006 #7
In the figures below, ∆HKM ~ ∆RTV, and the area of ∆HKM
is equal to 10 square units. What is the area of ∆RTV?
A     30.625 square units
B     87.5 square units
C     21.875 square units
D     61.25 square units

Correct Answer - A            11-April 2006 #51
Brandon wants to reduce a figure that is 9 inches
tall and 16 inches wide so that it will fit on a 9-
inch-by-12-inch piece of paper. If he reduces the
figure proportionally, what is the maximum size
the reduced figure could measure?

11-Fall 2005 #38
Correct Answer - J          October 2005 #32
A rectangle has a length of 4 feet and a perimeter
of 14 feet. What is the perimeter of a similar
rectangle with a width of 9 feet?
A    36 ft
B    42 ft
C    108 ft
D    126 ft

Correct Answer - B        11-April 2004 #23
In ∆STR, QP and TR are parallel. If SQ = 6 units,
QT = 24 units, and the perimeter of ∆SQP is 20
units, what is the perimeter of ∆STR?
A 80 units
B    100 units
C    320 units
D    500 units

Correct Answer - B         11-July 2004 #33
In the figure, ∆QNP ~ ∆PQH, and NM = 12.5
centimeters. What is the area of ∆PQN?
A    20.48 cm2
B    25.00 cm2
C    24.31 cm2
D    37.99 cm2

Correct Answer - A     11-October 2005 #47
The owner of an amusement park created a circular maze
that has a diameter of 50 feet. If the owner doubles the
radius of the maze, which statement describes what will
happen to the circumference and area of the maze?

A The circumference and the area will double.
B The circumference and the area will quadruple.
C The circumference will double, and the area will quadruple.
D The circumference will quadruple, and the area will double.
Correct Answer - C              10-April 2006 #23
The scale of two similar quadrilaterals is 1:2.
The perimeter of the smaller quadrilateral is 80
centimeters. What is the perimeter of the larger

A    40 cm
B    80 cm
C    160 cm
D    320 cm

Correct Answer - C     10-Spring 2003 #55
The edges of a large cube are 4 times longer than
the edges of a small cube. How many times
greater is the volume of the large cube?

F    4 times
G    12 time
H    16 times
J    64 times

Correct Answer - J   10-Spring 2003 #28
Mr. Kelly’s company manufactures a cylindrical
soup can that has a diameter of 6 inches and a
volume of 226 cubic inches. If the diameter stays
the same and the height is doubled, what will
happen to the can’s volume?
A    It will remain the same.
B    It will double.
C    It will triple.

Correct Answer - B         11-April 2006 #3
Mr. Norstam has just released a weather balloon with a diameter
of about 3 feet. As the weather balloon rises, it will expand and
eventually burst because of the changes in the atmospheric
pressure. If the weather balloon rises and expands to 1.5 times its
diameter before it bursts, what will be its change in volume?
F     The volume will increase to less
than 2 times the original volume.
G     The volume will increase to
between 2 and 3 times the
original volume.
H     The volume will increase to
between 3 and 4 times the
original volume.
J     The volume will increase to
between 4 and 5 times the
original volume.
Correct Answer - H                    11-July 2006 #32
What is the volume of a similar rectangular box with
dimensions that are 3.5 times larger than the
dimensions of the rectangular box shown below?
F    5,880 in.3
G     17,836 in.3
H     20,580 in.3
J     1,680 in.3

Correct Answer - H         11-February 2006 #32
The radius of a spherical beach ball is 24 centimeters.
If another spherical beach ball has a radius 3
centimeters longer, about how much greater is its
surface area, to the nearest square centimeter?
A     37 cm2
B     113 cm2
C     1,923 cm2
D     24,542 cm2

Fall 2005 #55
Correct Answer - C           October 2005 #18
If the surface area of a cube is increased by a
factor of 4, what is the change in the length of the
sides of the cube?
F    The length is 2 times the original length.
G    The length is 4 times the original length.
H    The length is 6 times the original length.
J    The length is 8 times the original length.

Correct Answer - F             April 2004 #26
A rectangular solid has a volume of 24 cubic
decimeters. If the length, width, and height are
all changed to ½ their original size, what will be
the new volume of the rectangular solid?

A    3 dm3
B    4 dm3
C    6 dm3
D    12 dm3

Correct Answer - A        11-Spring 2003 #33

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