# CSET: Math II - Three Dimensional Geometry

## 8 terms

### Three Dimensional Geometry

or solid geometry, is concerned with shapes such as cubes, rectangular solids, prisms, cylinders, spheres, cones, and pyramids. We will be interested in the volumes and surface areas for these figures, which are often related to a two-dimensional side or cross-section of the figure.

### Cube

is a three-dimensional figure with six congruent square sides.

If s is the length of one of its sides, the volume of the
cube is given by V(s) =s3.

Since the cube has six square-shape sides, the surface area of a cube is given by F(s)=6s2.

### Rectangular Solid

The volume of the rectangular solid below would be the product of the length, width, and height.

The following are the formulas for volume of a rectangular solid and the surface area of a rectangular solid:

V = lwh
S = 2(lw + wh + lh).

### Prism

is a solid that has two congruent parallel bases that are polygons. The polygons form the bases of the prism and the length of the edge joining the two bases is called the height.

### Cyllinder

Area of bases = 2(π)(r2). Area of the side = (h)(2πr). Total Surface Area = 2πr2+(2πr)h.

### Sphere

is a solid with all its points the same distance from the center.

The formula for the volume of a sphere is:4/3πr^3

The formula for the surface area is:4πr^2

### Cone

The formula for the volume of a sphere is:1/3πr^2h

The formula for the surface area is:4πr^2

### Pyramid

Volume: 1/3 x area of base x height