Volume

The student is able to (I can):

Calculate the volume of prisms, cylinders, pyramids, and cones

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).

Volume Lets 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?

For any prism, whether right or oblique, the volume is

V = Bh

where h is the altitude, not the length of the lateral edge.

Likewise, for cylinders, it doesnt matter whether the cylinder is right or oblique, the volume is

V = Bh = pir2h

Examples Find the volume of each figure:

1.

2.

10 ft.

8 ft.

3 m

19 m

( )2 2B 3 9 m= pi = pi3V (9 )(19) 171 m= pi = pi

( )1 5B 50 172.052 tan36

= =

V = (172)(8) = 1376 ft3

The volume of a pyramid with base area B and height h is

1V Bh

3=

The volume of a cone is

21 1V Bh r h3 3

= = pi

Examples Find the volume of the following:

1.

2.

222 3B 3 yd

4= =

= =31V ( 3)(3) 3 yd

3

10 mm10 mm

13 mm

5 mm

12 mm(Pyth. triple)

21V (10 )(12)3

=

3400 mm=

2 yd

3 yd

2 yd

Examples 3.

4.

7 ft.

21 ft.2 31V (7 )(21) 343 ft

3= pi = pi

25 mi

20 mi

21V (10 )(25)3

= pi

32500 mi3

= pi