Geometry Regents Lomac 2015-2016
Date 3/23
due 3/24
3D: Cross Sections and Rotating 2D
Name ________________________________________ Per______
LO: I can solve problems involving volumes of General Cones and General Cylinders and can
determine shapes formed by rotating 2D shapes.
 DO NOW
 (1)
On the back of this packet
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Cross Sections of general cones
Can you make a connection between general cones and dilations? Explain your thoughts.
 (2)
Cross Sections of general cylinders and general cones
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Parallel cross sections of general cylinders are ________________________________
Parallel cross sections of general cones are ________________________________
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 (3)
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Cross Sections of . . .
The diagram below shows cross sections of a figure starting at the bottom of the figure with the diagram on the far
left and moving toward the top on the far right.
Describe at least one description of what the three dimensional figure looks like. (There are multiple answers that
are valid.)
 (4)
Rotating 2D shapes to make 3D shapes Use the cutout shapes to help you answer the questions from here on.
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Rotating around a point
VS.
Rotate TWO around point W.
(you choose the number of degrees)
Sketch the resulting figure.
Rotate TRE around TR
(rotate a full 360°)
Sketch the resulting figure.
T
T
W
Rotating around a segment
O
R
E
Describe the difference between the two figures you sketched.
Rotating around a point produces a _________________________________ figure while rotating around a
segment or line produces a ________________________________ figure.
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 (5)
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Rotating 2D shapes to form 3D shapes
If AN = 8, NT = 6, and AT = 10 and triangle ANT is rotated about segment AN, what shape will be formed? Sketch
the shape, label the measurments, and find the volume of the figure.
A
T
N
 (6)
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Rotating 2D shapes to form 3D shapes
Sketch the figure formed when sector DUG is rotated about segment UG. Describe the figure and find its volume if
the radius of sector DUG is 8. Leave your answer in terms of π.
D
U
 (7)
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G
Rotating 2D shapes to form 3D shapes
Sketch the figure formed when rectangle BLOX is rotated about segment LX. Describe the figure and find its
volume if BX = 2(BL) and the perimeter of BLOX is 192.
B
X
L
O
4
 (8)
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Rotating 2D shapes to form 3D shapes
Triangle ANT is rotated about segment AT, what shape will be formed? Sketch and describe the shape.
A
N
 (9)
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T
Rotating 2D shapes to form 3D shapes
Sketch the figure formed when rectangle BLOX is rotated about line m, which is the perpendicular bisector of BL .
Describe the figure and find its volume if BX is 87.3 cm and BL = 42.5 cm. Round to the nearest hundredth.
m
L
B
X
O
 (10) Rotating 2D shapes to form 3D shapes
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Sketch the figure formed when triangle ANT is rotated about line q which passes through point A. q ⊥ AN .
Describe the figure and find its volume if AN = 28 and NT = 11. Round to the nearest integer.
A
q
N
T
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 (6)
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 (7)
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Exit Ticket
ON THE LAST PAGE
Homework
Provide sufficient evidence for each response.
 (1)
 (2) When each shape below is rotated about the bold line, a 3D shape is formed. Name the shape for each
figure.
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 (7)
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Homework
internet
 (3)
(a)
(b)
 (4) Find the measure of x in each diagram below.
A
6
B
2
C
G
9
H
12
x
E
F
x
D
5
J
11
10
I
Exit Ticket
Name________________________________ Date ___________ Per______
9.5R
The LO (Learning Outcomes) are written below your name on the front of this packet. Demonstrate your achievement of
these outcomes by doing the following:
(1) The diagram below shows cross sections of a figure starting at the bottom of the figure with the diagram on the far left
and moving toward the top on the far right.
Write at least one possible description of what the three dimensional figure looks like.
(There are multiple answers that are valid.)
(2) What shape is formed when the triangle below is rotated about line m?
m
7
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DO NOW
Name________________________________ Date ___________ Per______
9.5R
(1) Cakes sold by Destiny’s Deserts are made in the shape of cones or cylinders. The cones are 6” in diameter and 6” tall
while the cylinders are 4” in diameter and 6” tall. Should Destiny charge the same amount for both cakes, charge more for
the cone cakes, or more for the cylinder cakes? Justify your answer based on the amount of ingredients she will need for
each cake. Start by sketching the two cake shapes and labeling them with their measurements. (Use the reference page on
the back of 9.0 to help you.)
(2) What about the cartoon is supposed to make people smile? How does the girl’s slicing technique relate to Cavalieri’s
Principle?