Getting ready for solid geometry

Let’s refresh some concepts that will come in handy as you start the solid geometry unit of the high school geometry course. You’ll see a summary of each concept, along with a sample item, links for more practice, and some info about why you will need the concept for the unit ahead.

This article only includes concepts from earlier courses. There are also concepts within this high school geometry course that are important to understanding solid geometry. If you have not yet mastered the Transformations properties and proofs unit, it may be helpful for you to review that before going farther into the unit ahead.

Area is the amount of space enclosed in a 2D figure. We'll find the area of bases and cross-sections of 3D figures as a first step toward finding their volume. Also, understanding the area of cross-sections will help us relate volumes of tricky figures to the volumes of more familiar figures.

For more practice, go to Area of a circle and Area of triangles.

Here are a few of the exercises where reviewing area might be helpful:

Volume is the amount of space enclosed in a 3D figure. We'll use the volumes of familiar solids, like right rectangular prisms, to help us find the volumes of more unusual figures, like prisms that lean to one side, all sorts of pyramids, and figures with different shapes of bases.

For more practice, go to Volume of cylinders, Volume of cones, Volume of spheres, and Volume word problems: fractions & decimals.

Here are a few of the exercises where reviewing the volume of solid figures might be helpful:

We'll also explore why several of these volume formulas work. Come back at the end of the unit to compare and contrast these examples and see how we could solve them with fewer different formulas.

Proportional relationships are two quantities where the ratio between the two quantities always stays the same.

Density is a kind of proportional relationship that relates some quantity (such as mass or number of people) to the volume or area of a region. When we apply density, we often need to compare the density below some value, such as keeping the mass of a loaded ship less than $1{,}000 \text{ kg}$1, comma, 000, start text, space, k, g, end text per cubic meter, so that the ship will float.

For more practice, go to Rates & proportional relationships.

Here is an exercise where reviewing how to compare proportional relationships might be helpful: