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) r2h
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)(42)(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
