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 | \(V = \frac{4}{3}\pi r^{3}\)
\(SA = 4\pi r^{2}\) | r= radius |
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 | \(V = \frac{1}{3}\pi r^{2}h\)
\(SA = \pi r^{2} + \pi rl\) | r= radius h= height l = slant height |
Pyramid | \(V = \frac{1}{3}Bh\)
\(SA = B + \frac{1}{2}(p)l\) | B = area of base h= height p = perimeter l = slant height |
