5/31/17 Week 9 Wednesday daily sheet:
Volume of other right prisms & cylinders
Daily aims:
 1. I can calculate the volume of right prisms that aren’t rectangular (e.g., triangular prisms, hexagonal prisms).
 2. I can calculate the volume of cylinders.
 3. I can work “backwards” from the volume of a non-rectangular right prism or cylinder to a missing
dimension.
Before lesson
Use the props on your table to help you.
During lesson
1a) How is a cylinder like a prism?
1b) How is a cylinder unlike a prism?
2a) What’s the volume formula for a right prism? (See
your formula sheet.)
2d) Why do some formulas have a lowercase “b” while
others have a capital “B”?
2b) What’s the volume formula for a cylinder?
2c) Can you find any relation between these formulas?
D. Stark 5/14/2017
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3) To the nearest cubic centimeter,
what’s the volume?
3.2 cm
5.8 cm
4) What’s the volume of a hexagonal prism with a
Base (B) of 18 in2 and a height (h) of 4 in?
3 in
5) What’s the volume? Express your answer as a
mixed number.
6a) What shape is the base of the figure shown?
6b) What’s the full name of this figure?
7) What’s the height of a cylinder that has a volume of
351.68 cm3 and a radius of 4 cm?
D. Stark 5/14/2017
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5/31/17 Week 9 Wednesday daily sheet:
Volume of other right prisms & cylinders
Before lesson
Use the props on your table to help you.
KEY
During lesson
1a) How is a cylinder like a prism?
-Both have 2 congruent, parallel bases at right
angles to the height.
-Both are the same all the way from one base
to the other.
1b) How is a cylinder unlike a prism?
-The Base of a cylinder is a circle, not a polygon.
-Also, prisms have rectangular lateral faces. In
contrast, a cylinder has a single, curved face
(Actually, if you “unwrap” a cylinder, you’ll find
that the face is a rectangle.)
2a) What’s the volume formula for a right prism? (See
your formula sheet.)
V = Bh
2b) What’s the volume formula for a cylinder?
V =  r 2h
2c) Can you find any relation between these formulas?
2d) Why do some formulas have a lowercase “b” while
others have a capital “B”?
Lowercase “b” indicates the base of a 2-d shape.
It’s the length of a line segment.
Uppercase “B” indicates the Base of a 3-d shape.
It’s the area of the polygon that forms the “bottom”
or “top” of certain 3-d shapes.
Both are really Bh since the Base of a cylinder
is a circle, and its area is given by  r2.
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3) To the nearest cubic centimeter,
what’s the volume?
5.8 cm
V = r2h
V = (3.14)(3.22)(5.8)
V = 186.49088 cm3
3.2 cm
Rounded to the nearest
cubic centimeter, the volume is
186 cm3
4) What’s the volume of a hexagonal prism with a
Base (B) of 18 in2 and a height (h) of 4 in?
V = Bh
V = (18)(4)
V = 72 in3
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First, we need to find the Base,
which is the area of the
triangle.
B = ½ bh
B = ½ (2 ½)(2 ½)
𝟐𝟓
B=
3 in
5) What’s the volume? Express your answer as a
mixed number.
𝟖
Now we can use the volume formula
V = Bh
𝟐𝟓
V = ( )(3)
V=
𝟖
𝟕𝟓
𝟖
=
6a) What shape is the base of the figure shown?
a triangle
6b) What’s the full name of this figure?
triangular prism
Be careful of prisms lying down on the job! The
bases of a prism are 2 congruent, parallel polygons.
The base isn’t always on the bottom though usually
math problem writers are nice and draw them so
they are. The base here is not a rectangle.
𝟑
9 in
𝟖
7) What’s the height of a cylinder that has a volume of
351.68 cm3 and a radius of 4 cm?
V =  r2 h
351.68 = (3.14)(42)(h)
351.68 = (3.14)(16)(h)
351.68 = 50.24h
𝟑𝟓𝟏.𝟔𝟖
h=
𝟓𝟎.𝟐𝟒
= 7 cm.
D. Stark 5/14/2017
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