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Aviation Maintenance Technician Handbook–General

FAA-H-8083-30B Version 2023
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Chapter 3

Mathematics in Aviation Maintenance

Formula: A square yard measures 1 yard by 1 yard. It also measures 3 ; feet by 3 feet. Therefore, one square yard also equals 9 square ; feet (that is, 3 × 3 = 9). To convert square yards to square feet, ; multiply by 9. To convert square feet to square yards, divide ; by 9. Refer to Figure 3-23, Applied Mathematics Formula

Sheet, for a comparison of different units of area.

Computing Volume of Three-Dimensional Solids

Three-dimensional solids have length, width, and height. There are many three-dimensional solids, but the most common are rectangular solids, cubes, cylinders, spheres, and cones. Volume is the amount of space within a solid. Volume is expressed in cubic units. Cubic inches or cubic centimeters are used for small spaces and cubic feet or cubic meters for larger spaces.

Rectangular Solid

A rectangular solid is a three-dimensional solid with six rectangular-shaped sides. [Figure 3-24] The volume is the

Figure 3-19. Trapezoid.
Figure 3-19. Trapezoid.
Figure 3-20. Circle.
Figure 3-20. Circle.
Formula: volume = length × width × height = l × w × h

In Figure 3-24, the rectangular solid is 3 feet by 2 feet by 2 feet.

Formula: The volume of the solid in Figure 3-24 is = 3 ft × 2 ft × ; 2 ft = 12 cubic feet.

Example: A rectangular baggage compartment measures 5 feet 6 inches in length, 3 feet 4 inches in width, and 2 feet 3 inches in height. How many cubic feet of baggage will it hold? First, substitute the known values into the formula.

Formula: v = l × w × h ; = 5'6" × 3'4" × 2'3" ; = 5.5 ft × 3.33 ft × 2.25 ft ; = 41.25 cubic feet

Cube

A cube is a solid with six square sides. [Figure 3-25] A cube is just a special type of rectangular solid. It has the same formula for volume as does the rectangular solid, which is

Formula: volume = length × width × height = L × W × H. Because all

of the sides of a cube are equal, the volume formula for a cube can also be written as:

Formula: volume = side × side × side = S3

Example: A large, cube-shaped carton contains a shipment of smaller boxes inside of it. Each of the smaller boxes is 1 ft × 1 ft × 1 ft. The measurement of the large carton is 3 ft × 3 ft × 3 ft. How many of the smaller boxes are in the large carton? First, substitute the known values into the formula.

Formula: v = l × w × h ; = 3 ft × 3 ft × 3 ft