Name:________________________________________________________________________________Date:_____/_____/__________
Now you know all
4 transformations!
GRAPH the following transformations, and identify where A “prime” would be:
Dilations (dilate as indicated below):
1. A dilation is a ___________________.
Multiply by the
scale factor!
A
2. Dilate by a scale factor of 3:
A (1, 3)
A’ ( ____ , ____ )
3. Dilate by a scale factor of ½:
A (1, 3)
A’ ( ____ , ____ )
Rotations (rotate as indicated below):
4.
A rotation is a ___________________.
5.
90° CLOCKWISE rotation:
A (-1, -3)
A’ ( ____ , ____ )
6.
180° COUNTER-CLOCKWISE rotation:
A (-1, -3)
A’ ( ____ , ____ )
7.
Switch x and y
with every turn!
270° CLOCKWISE rotation:
A (-1, -3)
A’ ( ____ , ____ )
I
(+,+)
II
(-,+)
A
III
(-,-)
IV
(+,-)
Reflections (reflect as indicated below):
8.
A reflection is a _________________.
Make sure to flip over
the correct axis!
9.
Reflection over the x-axis:
A (-7, -5)
A’ ( ____ , ____ )
C
10. Reflection over the y-axis:
C (-4, -3)
C’ ( ____ , ____ )
A
B
Translations (translate as indicated below):
11. A translation is a _________________.
This means 4 to the
right, and 5 down!
12. (4, -5) translation:
A (-3, 2)
A’ ( ____ , ____ )
13. (-2, 4) translation:
A (-3, 2)
A’ ( ____ , ____ )
A
NAME:
Math-7 NOTES
DATE: ______/_______/_______
What:
volume of prisms and cylinders
Why:
. . . so I can calculate the volume of both rectangular prisms and cylinders.
Vocabulary:
Rectangular Prism-- a 3-D figure that is comprised of six _____________ faces (a “box”).
Cube– a special type of rectangular ___________ where each face is a ___________________.
Cylinder– a 3-D figure with circular __________________ for both the top and the bottom.
Radius-- refers to the line segment that __________________________ in the center and
extends to the circumference line (edge).
Diameter– refers to the line segment that extends the entire way _______________ a circle.
The diameter splits the circle into two _____________ halves.
Volume— the measure of __________ occupied by a solid region, measured in _______ un.³
Where is Volume in real-life?
Key Words:
Fill
Hold
Pour
V = lwh
2)
5 cm
1)
14 cm
Volume of a PRISM:
3)
12 cm
3.5 cm
7 cm
Word Problem Example: MaryBeth is filling a sandbox with sand. If the
sandbox is seven feet in length, two feet in height, and four feet in width, how
much sand can the sandbox hold?
V = 𝛑 r²h
Volume of CYLINDERS:
6 cm
1)
2.5 cm
2)
10 cm
3)
4 cm
15 cm
4.5 cm
Word problem example: Joe is pouring coffee into his coffee mug. The
mug is 7 in. tall, and its bottom has a diameter of 4 in. How much coffee does
Joe’s mug hold?
Changing an attribute (length, width or height):
o
If ONE (and only one) attribute of a figure is changed, then the resulting
volume will change by the ________ amount!
In other words, if ONE attribute doubles, the volume will also _____________ !
Or, if ONE attribute is decreased by half, then the volume will also
____________ by half!
4 cm
Example:
12 cm
o
If the volume of the first figure is 64
cm³, then what is the volume of the
second figure? _____________________
Word problem example: Julie has a jewelry box that holds 60 in³ when filled.
Stephanie’s jewelry box has the same dimensions– except that its length is half
the length of Julie’s box. How much can Stephanie’s box hold?
Wrap-it-Up/ Summary:
1) Why is volume measured in cubic units?
2) What are some real-life applications of volume?
NAME: _________________________________________________________________________________DATE: ______/_______/_______
“Volume of Prisms and Cylinders”
Show your work!
30 mm
20 mm
3 mm
8 in
3 in
32 in
10 in.
15 ft. and
Changing Attributes:
Show your work!
1.
Jen has a mug that holds 600 cubic cm of liquid. If Sara’s mug has a congruent base,
but is half the height, what is the volume of Sara’s mug?
2.
A pool that is 30 ft long, 6 ft wide, and 5 ft deep holds 900 ft³ of water. Another pool
holds 1,800 ft³ of water. It is equal in size, but is a different depth. How deep must
it be?
3.
A jumbo sandbox holds 428 cubic ft of sand. Another sandbox is equal in size, but
is 1/4 the length. How much sand does the smaller box hold?
SOL PRACTICE
1.
3.
2.
4.
Show your work!
NAME: _________________________________________________________________________________DATE: ______/_______/_______
“Volume of Prisms and Cylinders”
Show your work!
Show your work!
Changing Attributes:
5. Jen has a mug that holds 800 cubic cm of
liquid. If Julie’s mug has a congruent base,
but is half the height, what is the volume of
Julie’s mug?
6. A pool that is 20 ft long, 8 ft wide, and 4 ft
deep holds 640 ft³ of water. Another pool
holds 1,280 ft³ of water. It is equal in size,
but is a different depth. How deep must it
be?
7. A jumbo sandbox holds 81 cubic ft of sand.
Another sandbox is equal in size, but is 1/3
the length. How much sand does the
smaller box hold?