2.2.9 Formulas of Solids

Usually basic formulas for spheres, cubes, cones, and cylinders are fair game for the Number Sense test. In order to solve these problems, memorize the following table:

Type of Solid	Volume	Surface Area
Cube	$s^3$	$6s^2$
Sphere	$\frac{4}{3}\pi r^3$	$4\pi r^2$
Cone	$\frac{1}{3}\pi r^2 h$	$\pi r l + \pi r^2$
Cylinder	$\pi r^2 h$	$2\pi r h + 2\pi r^2$

(In the above formulas, $s$ is the side-length, $r$ is the radius, $h$ is the height, and $l$ is the slant height.)

In addition to knowing the above formulas, a couple of other ones are:

• Face Diagonal of a Cube = $s\sqrt{2}$
• Body Diagonal of a Cube = $s\sqrt{3}$

Problem Set 2.2.9