The student can calculate the volumes of prisms, cylinders, pyramids, and cones. The document defines different types of prisms and their components. It explains that the volume formula for any prism or cylinder is the base area multiplied by the height or altitude, regardless of whether it is right or oblique. Formulas are provided for calculating the volumes of pyramids and cones. Several examples are worked through applying the volume formulas to different shapes.

1. Volume
The student is able to (I can):
• Calculate the volume of prisms, cylinders, pyramids, and
cones

2. right prism
oblique prism
altitude
A prism whose faces are all rectangles.
A prism whose faces are not rectangles.
A perpendicular segment joining the planes
of the bases (the height).

3. Volume Let’s consider a deck of cards. If a deck is
stacked neatly, it resembles a right
rectangular prism. The volume of the prism
is
V = Bh,
where B is the area of one card, and h is
the height of the deck.
If we shift the deck so
that it becomes an
oblique prism, does it
have the same number
of cards?

4. For any prism, whether right or oblique, the
volume is
V = Bh
where h is the altitude, not the length of
the lateral edge.

5. Likewise, for cylinders, it doesn’t matter
whether the cylinder is right or oblique, the
volume is
V = Bh = πr2h

6. Examples Find the volume of each figure:
1.
2.
10 ft.
8 ft.
3 m
19 m
( )2 2
B 3 9 m= π = π
3
V (9 )(19) 171 m= π = π
( )
1 5
B 50 172.05
2 tan36
 = = 
° 
V = (172)(8) = 1376 ft3

7. The volume of a pyramid with base area B
and height h is
1
V Bh
3
=
The volume of a cone is
21 1
V Bh r h
3 3
= = π

8. Examples Find the volume of the following:
1.
2.
2
22 3
B 3 yd
4
= =
= = 31
V ( 3)(3) 3 yd
3
10 mm
10 mm
13 mm
5 mm
12 mm
(Pyth. triple)
21
V (10 )(12)
3
=
3
400 mm=
2 yd
3 yd
2 yd

9. Examples 3.
4.
7 ft.
21 ft.
2 31
V (7 )(21) 343 ft
3
= π = π
25 mi
20 mi
21
V (10 )(25)
3
= π
32500
mi
3
= π