Outcome 6.1 Construction Math: Measurement, Geometry, Scaling, and Conversions

Surface Area

The amount of 'skin' on the outside of a three-dimensional object.

Volume

The amount of 'space' inside a three-dimensional object.

Rectangular Prism Volume Formula

$V=L \times W \times H$ where $L$ is length, $W$ is width, and $H$ is height.

Cylinder Volume Formula

$V=\tau r^2 h$ where $r$ is the radius and $h$ is the height.

Triangular Prism Volume Formula

$V=\frac{1}{2}b h_{\triangle} L$ where $b$ is the triangle base, $h_{\triangle}$ is the triangle height, and $L$ is the prism length.

Precision

The level of detail in a measurement, indicated by rounding to a specified level.

Rounding

The process of adjusting a number to reduce the number of digits.

Concrete Volume Measurement

Typically calculated in cubic yards ($yd^3$) for ordering.

Paintable Wall Area Calculation

Calculated as perimeter times height of the walls.

Architectural Scale

A scale used for building plans expressing dimensions like 'inches on paper to feet in real life'.

Engineer’s Scale

A scale based on equal divisions per unit length, often read as feet per inch.

Similar Triangles

Triangles that have the same shape and proportional side lengths.

Right-Triangle Trigonometry

Involves using angles to find unknown lengths using functions like $\tan(x)$.

Grade Rod

A graduated rod used to read elevations when working with a builder’s level.

Builder’s Level

An instrument used to establish level lines and consistent elevations.

Measuring Cups

Used for measuring volumes in mixing materials like paint or concrete.

Cubic Feet to Cubic Yards Conversion

To convert from cubic feet to cubic yards, use the factor $1 \text{ yd}^3 = 27 \text{ ft}^3$.

Board Foot

A volume measurement for lumber, equivalent to $144 \text{ in}^3$.

Percent Grade

The ratio of rise to run multiplied by 100 to express slope as a percentage.

Unit Conversion

The process of changing a measurement from one unit system to another.

Common Area Conversion

$1 \text{ yd}^2 = 9 \text{ ft}^2$.

Fraction Addition Example

Adding $7 \frac{3}{8} \text{ in} + 4 \frac{11}{16} \text{ in}$ requires a common denominator.

Decimal to Fraction Conversion

To convert $0.375$ to a fraction, recognize it as $\frac{3}{8}$.

Waste Factor Calculation

To account for waste, multiply the needed amount by $1 + p\text{ (decimal percent)}$.

Right Triangle Rule

In a right triangle, the relationship is given by $a^2 + b^2 = c^2$, with $c$ being the longest side.

Measuring Tool Selection

Choosing a tool based on the measurement task, such as a tape measure for long distances or a level for elevations.