9.5R 3D Rotating Shapes and Practice Problems

Geometry Regents Lomac 2015-2016 Date 3/23 due 3/24

1 3D: Cross Sections and Rotating 2D 9.5R

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 On the back of this packet

(1) Cross Sections of general cones calculator 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) Cross Sections of . . . calculator 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.

Rotating around a segment

Rotate TWO around point W. (you choose the number of degrees) Sketch the resulting figure.

T

Rotate TRE around TR (rotate a full 360?) Sketch the resulting figure.

T

W

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) Rotating 2D shapes to form 3D shapes calculator 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

N

T

(6) Rotating 2D shapes to form 3D shapes calculator 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 .

D

U

G

(7)

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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

L

X

O

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(8) Rotating 2D shapes to form 3D shapes calculator Triangle ANT is rotated about segment AT, what shape will be formed? Sketch and describe the shape.

A

N

T

(9)

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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

B

L

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

 (6) Exit Ticket

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ON THE LAST PAGE

(7) Homework

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Provide sufficient evidence for each response.

(1)

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(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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