Oh no, here we go again.

Theorem 11-5: Cavalieri’s Principle

If two space figures have the same height and the same cross-sectional area at every level, then they have the same volume.

Example:

32

32 2

6

A=lw

A=32A=6 units2

A=lw

A=32A=6 units2

Since they all have the same area, then they have the same volume.

A=.5b h

A=.5 62A=6 units2

Theorem 11-6: Volume of a Prism

The volume of a prism is the product of the area of the base and the height of the prism.

V=Bareah

Example:

32

32 2

6

A=lw

A=32A=6 units2

A=lw

A=32A=6 units2

A=.5bh

A=.562A=6 units2

10 10 10

V=Bh

V=610

V=60 units3

V=610

V=60 units3

V=610

V=60 units3

Theorem 11-7: Volume of a Cylinder

The volume of a cylinder is the product of the area of the base and the height of the cylinder

V=Bareah

V=r2h

Example:

8 cm

3 cmV=r2h

V=(3cm)2(8cm)V=(72cm3)

V=804.2cm3

Volume of

Composite Space Figure

Find the volume of each figure and then add the volumes together.

Example:

12 in.4 in.

17 in.

12 in.4 in.

11 in.

4 in.6 in.

V = r2h( )/2V = (·62·4)/2V = 226in3

V = lwh

V = 12411

V = 528in3

V=226in3+528in3

V=754in3