Geometry 12.4 Volume of Prisms and Cylinders

**Volume of a solid** is the number of cubic units contained in its interior.

**Volume Congruence Postulate** - if 2 polyhedra are congruent, then they have the same volume.

**Volume Addition Postulate** - the volume of a solid is the sum of the volumes of all its nonoverlapping parts.

**Cavalieri’s Principle** - if 2 solids have the same height and the same cross-sectional area at every level, then they have the same volume.

**Volume of a Right Prism = Bh**

B = Area of the base

h = height of the solid

**Volume of a Cylinder** = Bh = (*pi*) *r*^{2}*h*

Example:

You have a right prism with a length of 5 cm, a width of 4 cm, and a height of 8 cm. What is it’s volume?

V = Bh = (5)(4)(8) = 160 cubic cm

Example:

You have a right cylinder with a diameter of 8 feet and a height of 13 feet. What is it’s volume?

V = Bh the radius will be 1/2 of 8 = 4 feet so

V = (*pi*)(4^{2})(13) = 208(*pi*) cubic feet or about 653.45 cubic feet.

Homework: #43 pg. 746; #10-19, 21-24, 28-32 even, 36-42 even, 45-49, 51-55, 57-59