Solid Geometry (3-D) Flashcards
Cube fast facts
let ∂, w, and h represent the length, width, and height, respectively, of a rectangular solid. If the rectangular solid is a cube, then ∂=w=h, and so each edge has the same length, which is represented by e.
Formula for the volume of a rectangular solid =
Volume of Rectangular Solid = ∂wh
Volume of a cube =
V = eee = e^3
Surface Area (A) of a Rectangular Solid
A = 2(∂+w+h)
Surface Area of a cube =
A cube = 6e^2
Diagonal of a box =
is a line segment joining a vertex on the top of the box to the opposite vertex on the bottom. A box has 4 diagonals, all the same length .
The diagonal of a box is the…
longest line segment that can be drawn between two points on the box.
If the dimensions of a box are ∂, w, and h, and if d is the length of a diagonal, then…
- ) d^2 = ∂^2 + w^2 + h^2
2. ) d = √( ∂^2 + w^2 + h^2 )
If h and r represent the height and the radius of the circular base of a cylinder, then the formulas for the volume (V), surface area (A), and total area (T) of the cylinder are:
- ) V = πr^2h [Note: this is the area of the circular base multiplied by the height]
- ) A = 2πrh [Note: This is the circumference of the circular base multiplied by the height.]
- ) T = 2πrh + 2πr^2
How many edges does a cube have?
A cube has 12 edges.
How many faces does a cube have?
A cube has 6 faces.
What are the two ways to express the volume of a cube with an edge length of one foot?
- ) (1 foot)^3 = 1 cubic foot
2. ) (12 inches)^3 = 1,728 cubic inches
The surface area of a cylinder is given by A =
A = 2πrh
Volume of a cylinder =
V=π(r^2)h
Even if you know the height of a cylinder what is still necessary to determine the volume?
The Radius !
