9.3+Volume

Section 9.3 - Volume
Volume is measured in cubic units. Picture a block that is 1 inch long on each side. That would be one cubic inch or 1 inch cubed. How many of those cubic inches could fit inside a suitcase, or a swimming pool?

For rectangular objects, (or really anything with a flat surface), volume is related to area. If you measure the area of a piece of paper laying on the table, you multiply the length times the width. Say the paper has an area of 80 square inches. But then imagine if the paper was 1 inch thick as well. You could fit 80 cubes on the piece of paper, so the volume of the paper at 1 inch thick would be 80 cubic inches. But if the paper were two inches thick, you could fit two layers, or 160 cubic inches.

A rectangular shape that has height as well is said to be "cuboid", or a "rectangular solid". ** The formula for volume of a cuboid or rectangular solid is length X width X height. ** Volume is always expressed in cubic units.


 * Volume of a Cylinder**

A cylinder is something that is round, like a can, and flat on both ends. A length of pipe could be considered a cylinder, even a worm kind of has that shape. Using the same concept as the 2-inch thick piece of paper above, think of a circle on the table that is then raised to be several inches tall. Although the formula for the volume of a rectangular shape is length times width times height, it could also be described as (the area of the base) times (the height). If that same concept is transferred to the cylinder, if you find the area of the circle and multiply it by the height (or length if it is laying down), you will have the volume.


 * The formula for the volume of a cylinder is (pi)(radius)(radius)(height). **


 * Volume of Other Shapes**

A **cone** is exactly 1/3 the size of the cylinder it fits into. The formula, then is (1/3)(pi)(radius)(radius)(height).

A **sphere** is (4/3)(pi)(radius)(radius)(radius).


 * Chapter Nine Practice Problems**

**Where to from here?**
9.1 Perimeter and Circumference 9.2 Area 9.3 Volume Chapter Nine Summary Chapter Nine Homework