Surface Volume Solids

Overview

Engineering reference data for Surface Volume Solids in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Additional Formulas

The following formulas complement those in the Key Formulas section for calculating properties of common geometric solids.

Diagonal of a Cube Face $d_s = a \sqrt{2}$ where $d_s$ is the diagonal of a cube face (m, ft) and $a$ is the side length (m, ft).

Cuboid (Rectangular Prism) $V = a \cdot b \cdot c$ $A_0 = 2(ab + ac + bc)$ $d = \sqrt{a^2 + b^2 + c^2}$ where $V$ is volume, $A_0$ is surface area, $d$ is the space diagonal, and $a$, $b$, $c$ are the length, width, and height (m, ft).

Cylinder $V = \pi r^2 h = \frac{\pi}{4} d^2 h$ $A = 2\pi r h + 2\pi r^2$ where $V$ is volume, $A$ is total surface area, $r$ is radius, $d$ is diameter, and $h$ is height (m, ft).

Hollow Cylinder $V = \frac{\pi}{4} h (D^2 - d^2)$ where $V$ is volume, $h$ is height, $D$ is outer diameter, and $d$ is inner diameter (m, ft).

Pyramid $V = \frac{1}{3} h A_1$ where $V$ is volume, $h$ is the perpendicular height, and $A_1$ is the area of the base (m², ft²). The surface area is the sum of the areas of all triangular faces plus the base area.

Frustum of a Pyramid $V = \frac{h}{3} \left( A_1 + A_2 + \sqrt{A_1 A_2} \right)$ where $V$ is volume, $h$ is the perpendicular height, and $A_1$, $A_2$ are the areas of the two parallel bases (m², ft²).

Cone $V = \frac{1}{3} \pi r^2 h$ $A = \pi r l + \pi r^2$ $l = \sqrt{r^2 + h^2}$ where $V$ is volume, $A$ is total surface area, $r$ is base radius, $h$ is height, and $l$ is the slant height (m, ft).

Frustum of a Cone $V = \frac{\pi}{12} h (D^2 + D d + d^2)$ where $V$ is volume, $h$ is height, $D$ is the larger base diameter, and $d$ is the smaller base diameter (m, ft). The slant height $m$ can be found via $m = \sqrt{((D-d)/2)^2 + h^2}$.

Sphere Data Table

This table provides pre-calculated surface areas and volumes for spheres with common fractional diameters (in inches). It is useful for rapid reference in applications involving small spherical components.

Interactive Charts

References

• Original Source