# Surface Area and Volume Terms

## Get down with the lingo

### Apothem

The distance from the center of a regular polygon to the midpoint of one side.

### Cone

A three-dimensional solid with a circular base and one vertex. We prefer to think of it as the waffle thing that ice cream comes in.

### Cross-Section

The two-dimensional shape you get when you chop up a three-dimensional one.

### Cylinder

Two parallel congruent circles whose circumferences are connected by a curvy rectangle.

### Density

A ratio that tells us how much stuff (mass) is 'packed in' a certain amount of space (volume).

### Euler's Formula

The formula relating faces, vertices, and edges of polyhedrons. In equation form, it's F + V = E + 2. In powder form, it tastes great in milk (not really).

### Hemisphere

Exactly half of a sphere. True story.

### Lateral Area

The area of the faces on a solid that aren't the base or bases. Or, in the case of cylinders and cones, the area of whatever isn't a flat circle.

### Ordered Triple

Three numbers that represent a position in actual three-dimensional space. Only the Tooth Fairy and Santa Claus can be imaginary in the 3D world, so they have to be real numbers.

### Polyhedron

"Many faces." We're talking more than just Professor Quirrell status. A polyhedron is any 3D solid that is made of entirely flat surfaces connected by edges and vertices. Sorry spheres, cylinders, and cones.

### Prism

Two parallel congruent polygons connected by lateral faces. Not "prison" in a French accent.

### Pyramid

Those huge stone buildings that the Egyptians built. It's basically a solid (definitely not a liquid or a gas) with a non-curvy shape for the base and one tip at the top.

### Regular Prism

A prism with bases that are regular polygons. Also, a prism that has daily scheduled trips to the potty.

### Similar Solids

Two solids that have the same shape but not necessarily the same size. All their angles must be the same and their heights and edges must have the same proportions.

### Sphere

A ball. It's a central point that includes all the points a certain distance away from it in space. It's like a circle—but in 3D.

### Surface Area

The total 2D area on the outside of a 3D solid, a.k.a. the amount of gift-wrapping paper it takes to cover all of particular shape. You can use newspaper instead of gift-wrapping paper; it's a lot cheaper.

### Volume

The amount of three-dimensional space that an object takes up. Or what your mom asks you to turn down when you're listening to "that noise you kids call music nowadays."