Properties of Three-Dimensional Shapes - Trivium Test Prep Online Courses

# Properties of Three-Dimensional Shapes

## Properties of Three-Dimensional Shapes

Three-dimensional objects, such as cubes, can be measured in three dimensions (length, width, and height). Three-dimensional objects are also called solids, and the shape of a flattened solid is called a net.

The surface area (SA) of a three-dimensional object can be figured by adding the areas of all the sides. Surface area is measured in square units (e.g., m2 or ft2). Volume (V) is the amount of space that a three-dimensional object occupies. Volume is measured in cubic units (e.g., mm3 or ft3).
Three-Dimensional Shapes and Formulas
Shape
Formula
Variables
Prism
$$V = Bh$$ $$SA = 2lw + 2wh + 2lh$$ $$d^{2} = a^{2} + b^{2} + c^{2}$$
B = area of base
h = height
l = length
w = width
d = longest diagonal
Cube
$$V = s^{3}$$ $$SA = 6s^{2}$$
s = cube edge
Sphere
$$V = \frac{4}{3}\pi r^{3}$$ $$SA = 4\pi r^{2}$$
Cylinder
$$V = Bh = \pi r^{2}h$$ $$SA = 2\pi r^{2} + 2\pi rh$$
B = area of base
h = height
l = slant height
Cone
$$V = \frac{1}{3}\pi r^{2}h$$ $$SA = \pi r^{2} + \pi rl$$
$$V = \frac{1}{3}Bh$$ $$SA = B + \frac{1}{2}(p)l$$